1. The probability mass function of a discrete random variable X is defined as p(x) =...

1. The probability mass function of a discrete random variable X is defined as p(x) = ax for x = 1, 2, 4, 8 (p(x) =0 for all other values) then the value of a is?

2. Let X be a discrete random variable with Var(X) =6.0 and E(X2) = 17.00. Then: E(X) = ?

3. If X is a binomial random variable with parameters n and p, i.e. X ~ b(x; n, p), then the expected value of X is E(X) = __________ and the variance is Var(X) = ___________

4. X is a continuous random variable, f(x) is the probability density function (pdf) of X, and F(x) is the cumulative distribution function of X. Then for any two numbers a and b with a < b, which of the following are true? Circle all correct answers.

A. P(a<-X<-b)=F(a)-F(b). ( - equals)

B. P(X>a)=1-F(a)

C. F(x)=(x-a)/(b-a)

D. P(X>b)=F(b)-1

5. If X is a normally distributed random variable with a mean of 36 and a standard deviation of 12, then the probability that X exceeds 36 is: A. .5000 B. .6250 C. .3750 D. None of the above

Expert Solution

orchestra answered 1 year ago

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