Throughout this problem use the following function: if x < 0 f(x) = if 0 < x < 2 if x > 2 (a) For what value of c is f(x) a probability density function? (b) If f(x) (with the value of c you computed in part (a)) is the probability density function for the continuous, random variable X, compute P(X > 1). (c) What is the mean (µ) of this probability density function f(x)?

Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply:   x P(X=x) 0 0.6 1 0.01 2 0.14     x P(X=x) 0 310 1 110 2 25     x P(X=x) 0 18 1 14 2 58     x P(X=x) 0 0.13 1 0.09 2 0.45 3 0.27 4 0.06     x P(X=x) 0 −15 1 310 2 12 3 310 4 110     x P(X=x) 0 12 1 18 2 38

Suppose you have the probability density function if 3 < x < 9 f(x) otherwise Find the cumulative distribution function of X. Select an answer ♥ F(x) if Select an answer if Select an answer Note: When writing your piecewise function, start with the left-most interval.

The graph to the right is the uniform probability density function for a friend who is x minutes late (a) Find the probability that the friend is between 5 and 25 minutes late (b) it is 10 AM. There is a 30% probability the friend will arrive within how many minutes? (a) The probability that the friend is between 5 and 25 minutes late is (Type an integer or a decimal Round to three decimal places as needed.) (b) There is a 30% probability the friend will arrive within minutes (Type a whole number) Ang 100 10 20 30x Tem