Using the probability distribution listed, 01234 P(x) 0.15 0.20 0.30 0.25 0.10 a
ID: 3349879 • Letter: U
Question
Using the probability distribution listed,01234 P(x) 0.15 0.20 0.30 0.25 0.10 a. Find the mean, variance and standard deviation b. Find P(x is no more than 3) ? c. Find P(x is at least 2) ? d. Find P(x < 2 or x >2) ? Using the probability distribution listed,
01234 P(x) 0.15 0.20 0.30 0.25 0.10 a. Find the mean, variance and standard deviation b. Find P(x is no more than 3) ? c. Find P(x is at least 2) ? d. Find P(x < 2 or x >2) ? Using the probability distribution listed,
01234 P(x) 0.15 0.20 0.30 0.25 0.10 a. Find the mean, variance and standard deviation b. Find P(x is no more than 3) ? c. Find P(x is at least 2) ? d. Find P(x < 2 or x >2) ?
Explanation / Answer
A) mean = E(X) = 0 * 0.15 + 1 * 0.2 + 2 * 0.3 + 3 * 0.25 + 4 * 0.1 = 1.95
E(X2) = 02 * 0.15 + 12 * 0.2 + 22 * 0.3 + 32 * 0.25 + 42 * 0.1 = 5.25
Var(X) = E(X2) - (E(X))2 = 5.25 - 1.952 = 1.4475
Standard deviation = sqrt(1.4475) = 1.203
B) P(X is no more than 3) = 1 - P(X > 3) = 1 - P(X = 4) = 1 - 0.1 = 0.9
C) P(X > 2) = P(X = 2) + P(X = 3) + P(X = 4)
= 0.3 + 0.25 + 0.1
= 0.65
D) P(X < 2 or X > 2) = P(X < 2) + P(X > 2) = 1 - P(X = 2) = 1 - 0.3 = 0.7
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