Question

A car agency sells 50% of its inventory of a certain foreign car equipped with airbags.

1. Find a formula (or a table) for the probability distribution of the number of cars with airbags among the next 4 cars sold by the agency.

2. Find the cumulative distribution function F(x) of the random variable X defined above.

3. Using F(x), verify that f(2)=3/8 in this case.

Answer 1

The probability that an inventory of a certain foreign car equipped with airbags is:

p=0.50=1/2

1. Let X be number of cars with airbags among the next 4 cars sold by the agency.

Therefore,

X ~ Binom(n = 4, p = 0.50)

The probability mass function of X is:

; x=0,1,2,3,4.

P(X = 1) = (?)p" + (1 - p)(n==

2. The cumulative distribution function F(x) of the random variable X is:

F(X) =Σ P(X = i)

3. Using F(x), f(2) is given by:

f(2) = F(2) - F(1)

(2) - ΣΡΙx = i) - ΣΡΙx =) =0

f(2) = P(X = 0) + P(X = 1) + P(X = 2) - P(X = 0) + P(X = 1)

f(2)= P(X = 0) + P(X = 1) + P(X = 2) - P(X = 0) - P(X = 1)

f(2)= P(X = 2)

8(2) = (4)51-5

f(2) = -

པw = (2)

$f(2)=6*(\frac{1}{16})$

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