4. Compare the Chebyshev inequality and the exact probability for the event X ->c as a function of c for the following cases. (a) X is a uniform random variable in the intervall-b, b (b) X is a bi...
If x is a binomial random variable, compute p(x) for each of the following cases: (a) n=5,x=5,p=0.2 p(x)= (b) n=4,x=4,p=0.8 p(x)=
Problem 2, using Chebyshev's inequality, estimate the probability that a random variable X ~ Г (4, 10) satisfies |X - 0.42 0.2 Problem 3. For i.id. X1 , . . . , Xn ~ Exp(2), n = 200estimate from above
Problem 2, using Chebyshev's inequality, estimate the probability that a random variable X ~ Г (4, 10) satisfies |X - 0.42 0.2 Problem 3. For i.id. X1 , . . . , Xn ~ Exp(2), n = 200estimate from above
If x is a binomial random variable, compute P(x) for each of the following cases: (a) P(x≤1),n=4,p=0.5 P(x)= (b) P(x>2),n=9,p=0.5 P(x)= (c) P(x<8),n=9,p=0.5 P(x)= (d) P(x≥3),n=4,p=0.9 P(x)=
If x is a binomial random variable, compute P(x) for each of the following cases: (a) P(x≤4),n=6,p=0.6 P(x≤4)= (b) P(x>3),n=4,p=0.9 P(x>3)= (c) P(x<6),n=7,p=0.4 P(x<6)= (d) P(x≥4),n=5,p=0.5 P(x≥4)=
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 1), n = 4, p = 0.1 Probability = (b) P(X > 1), n = 6, p = 0.1 Probability = (c) P(X < 3), n = 6, p = 0.3 Probability = (d) P(X > 2), n = 3, p = 0.4 Probability =
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 3), n = 9, p = 0.3 Probability = (b) P(X > 4), n = 5, p = 0.3 Probability = (c) P(X<5), n = 7.p = 0.35 Probability = (d) P(X > 6), n = 7, p = 0.3 Probability =
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 1), n = 7, p = 0.3 Probability = (b) P(X > 5), n = 7, p = 0.1 Probability = (C) P(X < 6), n = 8, p = 0.5 Probability = (d) P(X > 2), n = 3, p = 0.5 Probability =
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 2), n = 9, p = 0.4 Probability = (b) P(X > 3), n = 8, p = 0.35 Probability = (c) P(X < 2), n = 5, p = 0.1 Probability = (d) P(X 25), n = 9, p = 0.5 Probability =
4. Suppose that N is a random variable having a conditional Poisson distribution with ability mass function prob- 1 (log 3) PN(i) i 1,2,3,... 2 i (a) Show that the mean of N is 3 log 3 1.6479, 2 and the variance of N is 3(log 3)2 3 log 3 0.7427. 2 4 (b) Calculate the probability P(N -4I 20). (c) Use the Bienaymé-Chebyshev inequality to give a lower bound for the probability that N takes values within 2 standard...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...