Answer to Question #237895 in Statistics and Probability for clarktzy

Question

In the 2019 midterm election, a pollster was assigned to interview the oldest male and female in various households. Each was asked whether he or she voted for Vico Sotto. If the male said “Yes” and the female said “No,” the pollster recorded YN. Construct the probability distribution of the number of YES answers then find the mean, variance and standard deviation.

Answer 1

Solution:

Mean $E(X)=\sum X.P(X)=0+\dfrac{1}{4}+\dfrac{1}{2}=0.25+0.5=0.75$

Variance $= E(X^2)-[E(X)]^2=\sum X^2P(X)-(0.75)^2=1.25-0.5625=0.6875$

Standard deviation$=\sqrt{variance}=\sqrt{0.6875}=0.8291$