Question

There are 10 students in class and the number of siblings in their families are given by {1,1,1,1,2,3,3,4,4,4}. Consider the experiment of randomly choosing one of these students and letting Y denote the number of siblings in this chosen student’s family. (a) Find the probability mass function (pmf) of Y and plot this pmf. (b) Find Pr{Y > 2}. (c) Find the mean, µ, of Y . (d) Find the standard deviation, σ, of Y . (e) Find the exact value of P(µ−2σ ≤ Y ≤ µ + 2σ}.

Answer 1

a. Check the attached image

b. The Pr(Y > 2) = ½

c. The mean is 2.4

d. The standard deviation is: 2.72

e. The exact value is 1 because it is certain from the given data that any probability will fall within that range.

Step-by-step explanation:

a. An image showing the step by step solution is attached.

b. P(Y > 2) = P(3) + P(4)

= 2/10 + 3/10 = 5/10 = ½

c. The mean is 2.4

d. The standard deviation is: 2.72

e. Check the attached image for the steps.