Question

Submitting an external tool Available Jul 29 at 12am - Jul 29 at 11:59pm 1 day apter 5 Jessica Salmeron-Uribe Due in 3 hours, 58 minutes. Due Wed 07/29/2020 11:59 pm The following table represents the probability of the number of cars owned by a college student. Give your answer to at least 3 decimal places. 0.49 XP(x) 0 1 0.35 2 0.12 3 0.04 a) Is this a valid discrete probability distribution? Se ect an answer b) Find the mean number of cars owned. c) Find the standard deviation of the number of cars owned. d) Find o? License Points possible: 1 This is attempt 1 of 3. Submit

Answer 1

Solution:

a) This is a valid probability distribution because

$0\leq P(x)\leq 1$

And

$\sum P(x)= 1$ both the condition are satisfied.

b) To find mean E(X)

E(X)=2* P(x)

E( X) = 0*0.49 + 1*0.35 + 2*0.12 + 3* 0.04

E(X ) = 0 + 0.35 + 0.24 + 0.12

Mean = E( X) = 0.71

The mean number of cars owned is 0.71

c) To find the standard deviations of number of cars owned

First we find

E(X?

$E(X^2) =\sum x^2*P(x)$

$\sigma= \sqrt E(X^2)-[E(X)]^2$

$\sigma= \sqrt 1.19-0.71^2$

$\sigma= \sqrt 1.19-0.5041$

$\sigma= \sqrt 0.6859$

$\sigma= 0.8281907$

$\sigma= 0.8282$

The standard deviations of number of cars owned is 0.8283

d) $\sigma^2= 0.6859$