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- 13. Answer the following for the probability distribution 1 f(x) = (2x + 1) (2x + 1) X= 0, 1, 2, 3 16 a. Find the mean and the variance. μ = b. EX²-4X+6) 0²=In which probability distribution would a random variable XX have E(X)=λE(X)=λ?(50) Let X be a random variable with p.d.f. k 1For the probability distribution, find a. X b. P(y> 2) c. F(y= 6) d. P(y = 6) e. f(y= 4) f. f(y= 6) g. F(y = 5.5) h. F(4) f. Mean of X f(y) = 0.05, 0.10, 0.15, 0.20, X, y= -2 y = -1 y = 0 y = 1 y = 2A random variable Z is normally distributed with mean and variance are 0 and 1 respectively. Determine the probability of P(√2 ≤ Z < √5)The discrete random variable X has the probability distribution given by: -1 1 2 3 P(X = x) 0.2 r 0.4r 0.2 c. What is the variance of the random variable X? Answer in exact fraction or exact decimals d. Find the variance of the random variable Y, where Y = 6 – 2X Answer in exact fraction or exact decimalssolve it properly.A random variable Z is normally distributed with mean and variance are 0 and 1 respectively. Determine the probability of P( √2Given that X has the probability distribution f(x) = 1 for r 0, 1, 2,3, and 4. 16 Find the moment-generating function (MGF) of this random variable. Use the MGF to determine p. ' Use the MGF to determine u.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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