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b) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = kx², 0 < x < 2 1, x ≥ 2 = {²x³² Determine the value of k. c) Let X be the random variable with the cumulative probability distribution: x < 0 } F(x) = {₁₂e-2x x ≥ 0 Determine the expected value of X. d) The random variable X has a Poisson distribution such that P(X= 0) = P(X= 1). Calculate P(X = 2).

b) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = kx², 0 < x < 2 1, x ≥ 2 = {²x³² Determine the value of k. c) Let X be the random variable with the cumulative probability distribution: x < 0 } F(x) = {₁₂e-2x x ≥ 0 Determine the expected value of X. d) The random variable X has a Poisson distribution such that P(X= 0) = P(X= 1). Calculate P(X = 2).

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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b) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {kx² 0 ≤x≤2 1 x ≥2 Determine the value of k. c) Let X be the random variable with the cumulative probability distribution: F(x) = {₁ - 8-²x; 0 x < 0 x ≥ 0 Determine the expected value of X. d) The random variable X has a Poisson distribution such that P(X = 0) = P(X = 1). Calculate P(X = 2).
Transcribed Image Text:b) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {kx² 0 ≤x≤2 1 x ≥2 Determine the value of k. c) Let X be the random variable with the cumulative probability distribution: F(x) = {₁ - 8-²x; 0 x < 0 x ≥ 0 Determine the expected value of X. d) The random variable X has a Poisson distribution such that P(X = 0) = P(X = 1). Calculate P(X = 2).
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