QuestionEcon2300assignment: Ch5 Quiz

Econ2300
assignment: Ch5 Quiz

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Exercise 5.12 METHODS AND APPLICATIONS
Suppose that the probability distribution of a random variable x can be described by the formula

P(x) = x
________________________________________
15

for each of the values x = 1, 2, 3, 4, and 5. For example, then, P(x = 2) = p(2) =2/15.

(a) Write out the probability distribution of x. (Write all fractions in reduced form.)

x 1 2 3 4 5

P(x) ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________

________________________________________

(b) Show that the probability distribution of x satisfies the properties of a discrete probability distribution.(Round other answers to the nearest whole number. Leave no cells blank – be certain to enter “0” wherever required.)

P(x) ? for each value of x.

(c) Calculate the mean of x. (Round your answer to 3 decimal places.)

µx

(d) Calculate the variance, ?2x , and the standard deviation, ?x. (Round your answer ?x2 in to 3 decimal places and round answer ?x in to 4 decimal places.)

?x2

?x

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Exercise 5.23 METHODS AND APPLICATIONS
Suppose that x is a binomial random variable with n = 5, p = 0.3, and q = 0.7.

(b) For each value of x, calculate p(x), and graph the binomial distribution. (Round final answers to 5 decimal places.)

p(0) = , p(1) = , p(2) = , p (3) = ,
p(4) = , p(5) =

(c) Find P(x = 3). (Round final answer to 5 decimal places.)

P(x=3)

(d) Find P(x ? 3). (Do not round intermediate calculations. Round final answer to 5 decimal places.)

P(x ? 3)

(e) Find P(x < 3). (Do not round intermediate calculations. Round final answer to 5 decimal places.)

P(x < 3) = P(x ? 2)

(f) Find P(x ? 4). (Do not round intermediate calculations. Round final answer to 5 decimal places.)

P(x ? 4)

(g) Find P(x > 2). (Do not round intermediate calculations. Round final answer to 5 decimal places.)

P(x > 2)

(h) Use the probabilities you computed in part b to calculate the mean, ?x, the variance, ? 2x, and the standard deviation, ?x, of this binomial distribution. Show that the formulas for ?x , ? 2x, and ?x given in this section give the same results. (Do not round intermediate calculations. Round final answers to µx and ? 2x in to 2 decimal places, and ?x in to 6 decimal places.)

µx

?2x

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