3) Fidelity records the number of X-Trails sold each day. This data is used in calculating the following probability distribution of daily sales: x P(x) 0 0.1 1 0.1 2 0.2 3 0.2 4 0.3 5 0.1 a. Find the cumulative distribution function (cdf). b. Find the probability that the number sold tomorrow will be between 2 and four (both inclusive) c. Find the probability that the number sold tomorrow will be between 2 and four (inclusive) d. Find the probability that the number sold tomorrow will be between 2 (inclusive) and four.
Answers
Given : Fidelity records the number of X-Trails sold each day. This data is used in calculating the following probability distribution of daily sales
x 0 1 2 3 4 5
P(x) 0.1 0.1 0.2 0.2 0.3 0.1
To Find : the cumulative distribution function (cdf).
probability that the number sold tomorrow will be between 2 and four (both inclusive)
probability that the number sold tomorrow will be between 2 and four (inclusive)
probability that the number sold tomorrow will be between 2(inclusive) and four
Solution:
x P(x) CF
0 0.1 0.1
1 0.1 0.2
2 0.2 0.4
3 0.2 0.6
4 0.3 0.9
5 0.1 1
probability that the number sold tomorrow will be between 2 and four (both inclusive)
P(2) + P(3) + P(4)
= 0.2 + 0.2 + 0.3
= 0.7
or P(≤4 ) - P( <2 ) = 0.9 - 0.2 = 0.7 ( P( <2 ) = P( ≤1 )
probability that the number sold tomorrow will be between 2 and four (both inclusive) = 0.7
probability that the number sold tomorrow will be between 2 and four (inclusive) = P(3) + P(4) = 0.2 + 0.3= 0.5
or = P(≤4 ) - P( ≤2 ) = 0.9 - 0.4 = 0.5
probability that the number sold tomorrow will be between 2(inclusive) and four = P(2) + P(3) = 0.2 + 0.2 = 0.4
or = P(<4 ) - P( <2 ) = 0.6 - 0.2 = 0.4
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