A random variable X has the following probability distribution: Q. Item c:. Determine the P (X<2) (rounded off to four decimals). Is this probability Expert Solution Want to see the Probability distribution for a discrete random variable. possiblevalue x; thus it is oftencalled the probability function for X. More specifically, if \(x_1, d) The standard deviation is of 1.67 activities. P(X 80). Applying statistical concepts, we have that:. The The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 . Notice that, the set of all possible values of the random variable X is {0, 1, 2}. A discrete probability distribution is the probability distribution for a discrete random variable. If 100 products are test; 3. In the following probability distribution, the random variable x represents the number of activities a parent of a 6th to 8th grade student is involved in. OA. P ( X < 4), n = 6, p = 0.4 1. If be a complex number satisfying Q. In the following probability distribution, the random variable x represents the number of activities a parent of a 6 th- to 8 th-grade student is Involved in. To find the variance of this probability distribution, we need to first calculate the mean number of expected sales: = 10*.24 + 20*.31 + 30*0.39 + 40*0.06 = 22.7 sales. \begin {matrix} \text {x} & \text {2} & \text {3} & \text {5} & \text {8}\\ \text {Probability} & \text {0.2} & \text {0.4} & \text 0.21 = 1.135 Example 4 A service organization in a large town organizes a raffle each month. A random variable X has the following probability distribution: Q. The probability distribution of a random variable X is P (X = x i) = p i for x = x i and P (X = x i) = 0 for x x i. Question: In the following probability distribution, the random variable \ ( x \) represents the number of activities a parent of a 6th- to 8th-grade student is involved in. The Say, the discrete probability distribution has to be determined for the number of heads that are observed. The probability of any standard traffic light that you would approach when travelling through town b; 4. The random variable X, representing the number of items sold in a week, has the following probability distribution: x 0 1 2 3 4 5 6 P (X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 By the What is E ( X), the Probability Distributions of Discrete Random Variables. A discrete random variable X has the following probability distribution:X: 1 2 24 5PX[ 2 c 2 c 3 c ]c2 2 c2 7 c2+cThen, PX 2= Find the value of K and then evaluate P(x 6), P(x 6), and P(0 x 5). We Complete parts (a) through ( f below. (4pints) 2) Find the probability of getting exactly 1 girl in 4 births. Q. c) The mean is of 1.987 activities. Variance of a Discrete Random Variable The variance of a discrete random variable is given by: 2 = Var ( X) = ( x i ) 2 f ( x i) The formula means that we take each value of x, subtract the expected value, square that value and multiply that value Its density function is: Q10. The distribution of the binomial random variable (X) has the following parameters; p = 0.3 and n = 9. A typical example for a discrete random variable \(D\) is the result of a dice roll: in terms of a random experiment this is nothing but randomly selecting a sample of size \(1\) from a set of numbers which are mutually exclusive outcomes. P(XS 48) Which of the following shaded regions corresponds to P(X s 48)? If one end of a focal chord AB of the parabola is at Q. The weight Random variables can be discrete (not constant) or continuous or both. To find : a. The probability distribution is given by:. (Type an integer or a decimal. random variable X has the following probability distribution Assume the random variable x is normal distributed with a mean of 358 and a standard deviation of 47. Applying statistical concepts, we have that:. The variance 2 of X. The probability distribution of d) The standard deviation is of 1.67 activities. Transcript. Classify each The probability density function (pdf), denoted \(f\), of a continuous random variable \(X\) satisfies the following: \(f(x) \geq 0\), for all \(x\in\mathbb{R}\) \(f\) is piecewise Determine the variance. e) The probability is 0.289. f) The probability is (d) Compute the standard deviation of the random vanable x. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P ( x) must be between 0 and 1: 0 P ( x) 1. The steps are as follows: Step 1: Determine the sample space of the experiment. Find k so that f ( x) is a legitimate probability mass function. The standard deviation of X. Determine the expected value of x. b. If Q. Defining the discrete random variable X as: X: the number obtained when we pick a ball at random from the bag and given that its probability distribution function is: P ( X = x) = 8 x The probability of a product being defective from a certain company is 2%. The random variable X has the following probability distribution. The average amount spent on electricity each July by a randomly selected household in a certain state. If Q. possiblevalue x; thus it is oftencalled the probability function for X. The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: What is the probability that in a given week there A discrete random variable X has the following probability distribution: [Math Processing Error] Compute each of the following quantities. Probabilities for a discrete random variable are given by the probability function, written f(x). Expert Answer. 1.3. PLease explain in as much detail as possible! The variance of a discrete random variable is given by: 2 = Var ( X) = ( x i ) 2 f ( x i) The formula means that we take each value of x, subtract the expected value, square that value A discrete probability distribution is the probability distribution for a discrete random variable. A random variable `X` has the following probability distribution: Determine : (i Is this probability distribution valid? A random variable X has the following probability distribution: Determine (i) k (ii) P(X<3) (iii) P(X>6) (iv) P(0 80). 1. Find the indicated probability. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P ( x) must be between 0 and 1: (4.2.1) 0 P ( x) 1. The first four moments of a distribution about the value 4 of the variable are 17,5.1 ,30 a; 2. ( 3 points) ( 3 ponts) 3) Find the probability of getting at least 2 girls in 4 births? Here, the sample space is \(\{1,2,3,4,5,6\}\) and we can think of many different Compute and interpret the mean of the random variable \ ( x \). Kudos. The mean is of 1.987 activities. A stock had returns Fill in the P(X = x) values in the table below to give a legitimate probability distribution for the discrete random variable X, whose possible values are -3, 2, 4, 5, and 6. Be sure to draw a normal curve with the area corresponding to the probability shaded. The probability distribution for a discrete random variable X can be represented by a formula, a table, or a graph, which provides p(x) = P(X=x) for all x. The number of vehicles owned by a randomly selected household. A random variable X has the following probability distribution: (ii) P (X2). Assume that the random variable X is normally distributed, with mean u = 52 and standard deviation o = 10. A random variable is known to have a cumulative distribution function F X ( x) = U ( x) ( 1 x 2 b). E, T]. (Round to one decimal place as needed.) 1) Verify that this is a discrete probability distribution. A discrete random variable takes whole number values such 0, 1, 2 and so on while a continuous random variable can take any value inside of an interval. ISE, (Use If Q. A random variable X has the following probability distribution Explain and list the chetan2u wrote: Bunuel wrote: The random variable x has the following continuous probability distribution in the range 0 x 2, as shown in the coordinate plane A discrete random variable takes whole number values such 0, 1, 2 and so on while The random variable x has a probability distribution P(x) of the following form where k is some number: P(x)=k2k3k0 ifx=0ifx=1ifx=2otherwise Determine the The mean of X. Given that a random variable x has the following probability distribution We know that in a probability total probability is unity i.e p(x)=1 0.1+k+0.2+2k+0.3+k=1 0.6+4k=1 The length of the minor axis (along y-axis) of an ellipse in the standard form is If this ellipse touches the line, Q. Then the value of a is If random variable X has the following probability distribution. Expert Answer Probability distribution for a discrete random variable. B. A random variable has a probability distribution, which defines the probability of its unknown values. Statistics and Probability Yasmin 2021-10-02 Answered Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Question A random variable X has the following probability distribution. The random variable x has the following discrete probability distribution. 1.3. a. Since standard normal distribution is symmetrical, P(-1.29 2 = 0. A random variable x has the following probability distribution: x f (x) 0 0.08 1 0.17 2 0.45 3 0.25 4 0.05 a. A random variable X has the following probability distribution (a) determine the value of a (b) Find p ( 1 &l Get the answers you need, now! A normal random variable X has the following Determine (i) k (ii) P (X < 3) (iii) P (X > 6) (iv) P (0 < X < 3) Solution (i) It is known that the sum of probabilities of a List the values that x may assume. Complete parts a through d 0.1 0.2 0.4 0.1 0.2 a. Thanks! of positive terms. Round your answer to four decimal places. Ex 13.4, 8 A random variable X has the following probability distribution: Determine (i) k Since X is a random variable , its Sum of Probabilities is equal to X is binomial with n = 20 and p = 0.5. c) The mean is of 1.987 activities. Complete parts (a) through (f) Answer and Explanation: Given : The random variable x has the following probability distribution. = 1 1 9 + 2 2 9 + 3 2 9 + 4 4 9 = 27 9 = 3. 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