STAT 204-Consider the following discrete probability distribution

STAT 204-Consider the following discrete probability distribution

Subject: Mathematics    / Statistics
Question

1.Consider the following discrete probability distribution:

X    -1.3    0    2.1    5.4    6.2
P(X)    0.19    0.18    0.15    0.24    0.24

a) What is P(X=0)?

b) What is P(X=0?X<5)?

Round your answer to at least 3 decimal places.

2. Identify each of the following statements as either TRUE or FALSE.

a) (Click for List) False True In a binomial distribution, the random variable X is a count of the number of successes.

b) (Click for List) True False If the probability of success is greater than zero, then the mean of a binomial random variable is greater than the variance.

c) (Click for List) False True The largest value a binomial random variable can be is n + 1.

d) (Click for List) False True In a binomial distribution, each trial can have one of two possible outcomes.

e) (Click for List) True False There are two parameters in a binomial distribution.

3. Consider the following discrete probability distribution:

X    -0.76    -0.015    0.71    1.0
P(X)    0.1    0.4    0.3    0.2

a) What is E[X]?

Round your answer to at least 3 decimal places.

b) What is Var[X]?

Round your answer to at least 3 decimal places.

4. Identify each of the following statements as either TRUE or FALSE.

a) (Click for List) True False In a geometric distribution, if the first success occurs on the Xth trial, then on the first X – 1 trials there must have been only a small number of successes.

b) (Click for List) True False If X is a geometric random variable, then the smallest value X can take on is 0.

c) (Click for List) True False The mean of X, a geometric random variable, is 1/p, where p is the probability of success on a single trial.

d) (Click for List) False True If the probability of success in a geometric distribution is greater than 0.5, then the variance is greater than the mean.

e) (Click for List) False True The geometric distribution is dependent upon two parameters.

5. Let X be a discrete random variable that follows a binomial distribution with n = 11 and probability of success p = 0.71.

What is P(X>7?X?9)?

Round your response to at least 3 decimal places.

6. According to the Statistics Canada website, the unemployment rate in Canada is approximately 8.0 % of the eligible workforce. If 25 members of the eligible workforce are randomly selected, what is the probability that exactly 4 of them are unemployed?

Round your response to 3 decimal places.