Assume random variable ? is uniformly distributed in the
interval (−?/2 ,?⁄ 2]. Define the random variable ?=tan (?), where
tan (∙) denotes the tangent function. Note that the derivative of
tan (?) is 1/(cos (?)2) .
a) Find the PDF of ?.
b) Find the mean of ?
.Define the random variable ?=1/?.
c) Find the PDF of ?.
Assume random variable ? is uniformly distributed in the interval (−?/2 ,?⁄ 2]. Define the random...
A random variable X is uniformly distributed on the interval [-TT/2.TT/2]. X is transformed to the new random variable Y = T(X) = 2 tan(X). Find the probability density function of Y. (Hint: (tan x)' = 1/cos2x, cos?(tan 1x) = 1/(1+x2)
1. Let U be a random variable that is uniformly distributed on the interval (0,1) (a) Show that V 1 - U is also a uniformly distributed random variable on the interval (0,1) (b) Show that X-In(U) is an exponential random variable and find its associated parameter (c) Let W be another random variable that is uformly distributed on (0,1). Assume that U and W are independent. Show that a probability density function of Y-U+W is y, if y E...
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems:
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems:
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2. The random variable X is uniformly distributed in the interval [4,8). Find the probability density function for random variable Y if Y 6X 12 3. Two independent random variables X and y are given with their distribution laws: 0.2 0.4 0.1 0.9 0.7 0.1 p. Find the distribution law and mode of the random variable Z-5XY 0.2
Let X be uniformly distributed in the unit interval [0, 1]. Consider the random variable Y = g(X), where c^ 1/3, 2, if x > 1/3 g(x)- (a) Compute the PMF of Y b) Compute the mean of Y using its PMF (c) Compute the mean of Y by using the formula E g(X)]9)fx()d, where fx is the PDF of X
X is a random variable uniformly distributed on [-3,1]. 1. Let Y = 2X – 1, find the pdf of Y. 2. Let Z = [X], find the pdf of Z. 3. What is the pdf of Y = [X + 3/?
Problem 6: 10 points Assume that X and Y are independent random variables uniformly distributed over the unit interval (0,1) 1. Define Z max (X. Y) as the larger of the two, Derive the C.DF. and density function for Z. 2. Define W min(X,Y) as the smaller of the two. Derive the C.D.F.and density function for W 3. Derive the joint density of the pair (W. Z). Specify where the density if positive and where it takes a zero value....
Problem 6: 10 points Assume that X and Y are independent random variables uniformly distributed over the unit interval (0,1) 1. Define Z-max (X, Y) as the larger of the two. Derive the C.D.F. and density function for Z. 2. Define Wmin (X, Y) as the smaller of the two. Derive the C.D.F. and density function for W 3. Derive the joint density of the pair (W, Z). Specify where the density if positive and where it takes a zero...
Suppose that Y=cos(X), where X is uniformly distributed over the interval [0, 2Pi]. Determine the pdf of the random variable Y.
Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e X has a density f(x) = { 1, 0<r<1 f (x)- 0, elsewhere μ+ơX, where-oo < μ < 00, σ > 0 (a) Find the density of Y (b) Find E(Y) and V(Y)