X is a random variable uniformly distributed on [-3,1]. 1. Let Y = 2X – 1,...
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean and variance of X. (2) Let Y 2X+3. Draw the PDF of Y [8 marks] 6 marks] [8 marks (3) Find the mean and variance of Y
Let X be a random variable with PDF fx(X). Let Y be a random variable where Y=2|X|. Find the PDF of Y, fy(y) if X is uniformly distributed in the interval [−1, 2]
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 X is uniformly distributed in the interval (-1/2, 1/2). Define the random variable Y = tan(X), where...
Let a random variable X be uniformly distributed between −1 and 2. Let another random variable Y be normally distributed with mean −8 and standard deviation 3. Also, let V = 22+X and W = 13+X −2Y . (a) Is X discrete or continuous? Draw and explain. (b) Is Y discrete or continuous? Draw and explain. (c) Find the following probabilities. (i) The probability that X is less than 2. (ii) P(X > 0) (iii) P(Y > −11) (iv) P...
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:
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3) Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
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...
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
Consider an exponentially distributed random variable X with pdf f(x) = 2e−2x for x ≥ 0. Let Y = √X. a. Find the cdf for Y. b. Find the pdf for Y. c. Find E[Y]. If you want to skip a difficult integration by parts, make a substitution and look for a Gamma pdf. d. This Y is actually a commonly used continuous distribution. Can you name it and identify its parameters? e. Suppose that X is exponentially distributed with...
Let there be U, a random variable that is uniformly distributed over [0,1] . Find: 1) Density function of the random variable Y=min{U,1-U}. How is Y distributed? 2) Density function of 2Y 3)E(Y) and Var(Y) U Uni0,1