1.Given a continuous random variable X with the density function

(a) Find the value of k.

(b) Find P(1

(c) Find the mean of X. 00

(d) Find the standard deviation of X.

2. A cell plume service provider wants to analyze the signal strengths of its network. Let X be the random variable that is the distance (in inikN) that a customer will he to the neawst cell phone tower. Analyzing their &Wiliam, the company finds that the probability density function is

(a) Find the mean of X.

(b) Find the standard deviation of X.

(c) The company is now interested in signal strengths. The company finds that the signal power (in mill watts) at a distance x from the lower is y?40/x ² . Given the probability density function for X in the previous part, what is the expected signal strength E(Y)?

3. Let Z be a standard normal random variable. Solve the following questions by using the standard normal table.

(a) P(?2.50 ? Z ?1.29)

(b) P(Z ? 1.37)

(c) P(Z ? ?0.69)

(d) P(|Z|

(e) Find z0.15.

kr 0x2 otherwise [(T) (x) = { 1 0 - {1/4 f(x)= 1/4 2x6 otherwise