continuous random variable X that can assume values between x = 1 and x = 3 has a density function given by f(x) = ½ a) Show that the area under the curve is equal to 1 b) Find P(2 < x < 2.25) c) Find P(x < 1.6)

Q1) CDF, PDF, Expectation and Variance The cumulative distribution function (CDF) of random variable Y is y 1. a) Find the probability density function, fy(y), of random variable Y. b) Show that f fy (y)dy = 1. c) What is E[Y]? d) What is VAR[Y]?

The continuous random variables X and Y are statistically independent and have marginal density functions fx(x) = 2x, 0 1. y2' Calculate the probability P(X < 0.5, Y < 2)

Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 0

Let X have the uniform distribution on the interval [1, 3]. Find the density function of Y =X^2.

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