Question

1. Random Variable: The variable X represents the number of goals scored by the soccer team Liverpool FC during all competitions of the 2018- 2019 season.

X: 0, 1, 2, 3, 4, 5

P(X): 0.13, 0.25, 0.23, 0.17, 0.17, 0.05

a. Does the above table represent a probability distribution for the variable X? Explain.

b. Calculate the mean value for the variable X.

c. What is the probability that they score 2 or more goals for a given game during that season?

2. Binomial Distribution Michael Jordan had a free throw percentage of 83.5 during his whole career. Let X represent the number of successful free throw attempts.

a. Calculate the probability that during ten free throw attempts he was successful in 7 of them.

b. Calculate the probability that during 10 attempts he was successful in only 2 of them.

c. Calculate the mean and standard deviation for the random variable X for 10 attempts.

d. Assume that you are a Sport Commentator, what information does the mean and standard deviation for the random variable X provide within this context? Explain.

Answer 1

1.

a. By definition of pmf ,

If the given function is a probability distribution function , then it satisfy the fallowing two conditions.

I) ; Fro all x

II)

Here ,

I) ; Fro all x

II)

The both conditions are satisfied.

Therefore , the given table represent a probability distribution for the variable X.

b. The mean value for the variable X is ,

c. Now , the probability that they score 2 or more goals for a given game during that season is ,