MaTugirõupieCompute the expected value of the discrete random variable.13. Let X be a discrete random variable with SuppeS= {1, 2, 3, 4}. Its pmf is given below.[1if x E the Support Sf (x)= {40,if x 4 the Support Sà14. Let Xbe a discrete random variable with Support S={1, 2}.ipmf is given below.if x E the Support Sf (x)={30,if x 4 the Support S15. LetXbea discrete random variable with Support S = {1, 2, 3, 4Its pmf is given below.)if x E the Support Sf(x)= {100,if x 4 the Support S.16LerX bediscret

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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UNIVERSITY OF BOTSWANA DEPARTMENT OF MATHEMATICS Question One MAT 271 TEST 1 Let a random variable W be given by WZ+Z+...+Zo where Z, are independent standard normal random variables for i = 1, 2, ..., 10. Find P(3.247W < 20.483) [7 marks] x-x Z = ก Question Two A boy flips a fair coin 100 independent times and a girl flips a fair coin 100 independent times. What is the probability that the boy will have 10 less tails than the girl? Question Three [7 marks] The random variable, X, representing the number of ice blocks in a drink, has the following probability distribution. H 4 5 6 7 f(x) = P(X = 1) 0.2 0.4 0.3 0.1 Find, using the normal approximation, the probability that in a sample of 36 drinks, the average number of ice blocks will be less than 5.5. [8 marks] P (W < 3.247) - P (W220.483) - 5.1 4-4-9 + -5 + - 5.2 253 1 p(x <5.5)=1 <)+(01)+5(04)+(0-3) + 7 (0.1) 1. (**)+(0,2)+5" (0.4)+6°² (0-3)+21 (0+1) 29.9 1=36 ०=०.११
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9.6 In a certain population the random variable Y has variance equal to 490. Two independent random samples, each of size 20, are drawn. The first sample mean is used as the predictor of the second sample mean. (a) Calculate the expectation, expected square, and variance, of the prediction error. (b) Approximate the probability that the prediction error is less than 14 in absolute value. Show Transcribed Text
Find these probabilities for a standard normal random variable Z. Be sure to draw a picture to check your calculations. Use the normal table or software. (a) P(Z - 1.1) (c) P(|Z| 0.7) (e) P(- 1.15Z - 1.1)= (Round to four decimal places as needed) (c) P(|Z| 0.7) = (Round to four decimal places as needed.) (e) P(-1.1sZ 12) =| (Round to four decimal places as needed )
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discrete random variable with Suppo Compute the expected value of the discrete random variable. Ler X be a discrete random variable with Suppe 13