Hw1,2

1. For 0

l. For 0 S x 1, let f (x) = kx(l x), where k is a constant. (a) Find the value of k such that fis a density function. (b) What is the mean value of this random variable? (c) What is the variance of this random variable? (d) Construct the cumulative distribution for this random variable. a Probability And Statistics for Engineers And Scientists, Hayter, A. (2007), Chapter 2 2. 'I A random variable X takes values between 4 and 6 with a probability density function f (x) = for 4 x 6 and f (x) = 0 elsewhere. (a) Check that the total area under the probability density function is equal to l. (b) What is x 5)? (c) Construct the cumulative distribution function. (d) What is the expected value of this random variable? (e) What is the variance of this random variable? (f) What is the standard deviation of this random variable? 1 xln(1.5)