(a). Find the value of ß that makes fx(r) a valid pdf. (b) Find the edf for the random variable X. (c) Find the probability that the random variable X is greater than 2.
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- 7. Let X be a continuous random variable with pdf f(x)=√ 04. Suppose that X has pdf f(x) = 3x² for 0 < x< 1. Find the pdf of the random variable Y = VX.B) Let the random variable X have the moment generating function e3t M(t) for -13. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probabilitymass function (PMF)y 0 1 2 3fY (y) 0.12 0.13 0.33 0.42(a) What is the probability a YSU student got exactly one ticket?(b) What is the probability a YSU student got at least one ticket?(c) Compute µY , the mean of Y .(d) Find the variance and standard deviation of Y .(e) What is the probability that Y exceeds its mean value?Suppose that Y is a uniform continuous random variable on the interval (1,11). Calculate the expected value of the random variable (Y− 1)². Use one decimal place accuracy.Suppose W is a random variable with the pdf f(w) = 3u3e-w³/343 for w≥ 0.1 If Y = -12W + 11, what is the pdf of Y? еLet X1, X2, X3, X4 be a random sample from the distribution with PDF f(x) = e¯", x > 0. Calculate the probability that second largest of these random variables is less than 2.5. Find the moment generating function of the exponentially distributed random vari- able with pdf Xe-, x≥0 and use it to evaluate the mean and variance of X.1.4 Let X be a continuous random variable with pdf, fx(x), and fx(t+5) = fx(5 – t) for all t> 0. Please provide the mean of X.Recommended textbooks for youGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill