If the probability density of X is given by
Where k is an appropriate constant, find the probability density of the random variable Y = 2X / 1+ 2X . Identify the distribution of Y, and thus determine the value of k.
Answer to relevant QuestionsIf the probability density of X is given by Find the probability density of Y = X3. Also, plot the graphs of the probability densities of X and Y and indicate the respective areas under the curves that represent P(1/2 < X < ...Consider the random variable X with the uniform density having α = 1 and β = 3. (a) Use the result of Example 7.2 to find the probability density of Y = | X|. (b) Find the probability density of Z = X4(=Y4). If X1 and X2 are independent random variables having the geometric distribution with the parameter θ, show that Y = X1 + X2 is a random variable having the negative binomial distribution with the parameters θ and k = 2. Let X and Y be two continuous random variables having the joint probability density Find the joint probability density of Z = X + Y and W = X. Prove the following generalization of Theorem 7.3: If X1, X2, . . ., and Xn are independent random variables and Y = a1X1 + a2X2 + · · · + anXn, then Where MXi(t) is the value of the moment-generating function of Xi at t. ...
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