# Question: Consider the density function of a random variable X defined

Consider the density function of a random variable X defined by

(a) Find the CDF corresponding to this density function. (Be sure you describe it completely.)

(b) Calculate the mean and variance.

(c) What is the probability that a random variable having this density will exceed 0.5?

(d) Consider the experiment where six independent random variables are observed, each random variable having the density function given above. What is the expected value of the sample mean of these observations?

(e) What is the variance of the sample mean described in part (d)?

(a) Find the CDF corresponding to this density function. (Be sure you describe it completely.)

(b) Calculate the mean and variance.

(c) What is the probability that a random variable having this density will exceed 0.5?

(d) Consider the experiment where six independent random variables are observed, each random variable having the density function given above. What is the expected value of the sample mean of these observations?

(e) What is the variance of the sample mean described in part (d)?

## Relevant Questions

A transistor radio operates on two 1 ½ volt batteries, so that nominally it operates on 3 volts. Suppose the actual voltage of a single new battery is normally distributed with mean 1 ½ volts and variance 0.0625. The radio ...Suppose the sample space Ω consists of the four points w1, w2, w3, w4, and the associated probabilities over the events are given by Define the random variable X1 by X1 (w1) = 1, X1 (w2) = 1, X1 (w3) = 4, X1 (w4) = 5, and ...Let X be a random variable with density (a) What value of K will make fX(y) a true density? (b) What is the CDF of X? (c) Find E(2X – 1). (d) Find variance (X). (e) Find the approximate value of P{X–bar > 0}, where X is ...Consider a parallel system consisting of two independent components whose time to failure distributions are exponential with parameters μ1 and μ2, respectively (μ1 ≠ μ2). Show that the time to failure distribution of ...Follow the instructions of Prob. 25.4-1 when using the following network. (a) Find all the minimal paths and cuts. (b) Compute the exact system reliability, and evaluate it when pi = p = 0.90. (c) Find upper and lower bounds ...Post your question