Let X have a U[0,1] distribution and Y have a Exp[1] distribution, what is the maximum expected value?
Let X have a U[0,1] distribution and Y have a Exp[1] distribution, what is the maximum...
Let U ~uniform(0,1). Let Y =−ln(1−U). hint: If FX (x) = FY (y) and supports x,y ∈ D, X and Y have the same distribution. Find FY (y) and fY (y). Now, it should be straight forward that Y follows distribution with parameter_____________-
U is Uniform distribution here
Let X ~ U[0,1] and Y = max {,x) (a) Is Y a continuous random variable? Justify (b) Compute E[Y]. (Hint: Note that when a (Hint: Note that when a-, max 1.a- , and when a > ļ, max | , a- ax {3a, and when a > a
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Let X have a uniform distribution on the interval (0,1) a. Find the probability distribution of Y-1 Enter a formula in the first box and a number in the second and third boxes corresponding to the range of y. Use * for multiplication, / for divison, for power and in for natural logarithm. For example, (3"у"e 5"y+2)+11*1n(y))/(4xy+3) 4 means (3y-e5 +2 + 11-in y)/(4y+3)4, Use e for the constant e g. e...
Let U have a U(0,1) distribution. describe how to simulate the outcome of a roll with a die using U. Define Y as follows: round 6U + 1 down to the nearest integer. What the popssible outcomes of Y and their probabilities?
7.4 Let X ~ U(-1,1) and Y = x2. a. What are the density, the distribution function, the mean, and the variance of Y: b. What is Pr[Y < 0.5]? 7.5 Let X – U(0,1), and let Y = eax for some a > 0. What are the density, the distribution function, the mean, and the variance of Y?
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].
5. Let X have the uniform distribution U(0, 1), and let the conditional distribution of Y, given X = x, be U(0, x). Find P(X + Y ≥ 1).
4) Suppose that Y~exp(8). Let X = ln(Y). Find the pdf of X. 5) Let Y and Y2 be iid U(0,1). Let S YY2. Find the pdf of S.
5. Let X have a uniform distribution on the interval (0,1). Given X = x, let Y have a uniform distribution on (0, 2). (a) The conditional pdf of Y, given that X = x, is fyıx(ylx) = 1 for 0 < y < x, since Y|X ~U(0, X). Show that the mean of this (conditional) distribution is E(Y|X) = , and hence, show that Ex{E(Y|X)} = i. (Hint: what is the mean of ?) (b) Noting that fr\x(y|x) =...
a. Let X ~ Uniform(0,1). Find the distribution function of Y =-21nX. What is the distribution of Y. Find P(Y> 0.01)