Compute the cdf and the density of y
Suppose that X has density fX(x) given below. fX(x) = x/2 if 0 < x < 2, 0 otherwise. Let Y = 1/(4X + 2) . (a) Compute the cdf and the density of Y . (Remember to be very explicit about all cases!) Plot them. (b) Compute the variance of Y and of Y2
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Let X1 and X2 be independent random variables, each having a (continuous) uniform distribution over (0; 1). Let the random variable M be de ned as M = max(X1;X2)
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Determine the conditional probability that the second light will be red given that the first light is red. (Show how you calculate this.) Are the events R1 and R2 independent? Justify your answer numerically.
Suppose that X has density fX(x) given below. fX(x) = x/2 if 0 < x < 2, 0 otherwise. Let Y = 1/(4X + 2) . (a) Compute the cdf and the density of Y . (Remember to be very explicit about all cases!) Plot them. (b) Compute the variance of Y and
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Determine if it is safe for a 225 lb worker to stand all the way to the right of the scissor jack with it fully extended.
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