Let the PDF of a continuous random variable X be defined as fx(x) = { 3x, 0 - а. 0.50 b. 0.30 С. 0.34 d. 0.48 O O
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- Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
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- Find the probability that the range of a random sample of size 4 from theuniform distribution having the pdf f(x) = 1, 0 < x < 1, zero elsewhere, is lessthan 12 .Let X be a random variable with exponential distribution having lambda=6 and let Y = 3X. a. Find P(X>0.25) b. Find the mgf of Y c. Find the pdf of YLet X be a continuous random variable with pdf