Studdy AI Logo
Math  /  Data & Statistics

QuestionThe table shows the probability distribution for a discrete random variable XX. a. Complete the table by finding the missing values of x⋅P(x)x \cdot P(x). Then compute the mean of the probability distribution. \begin{tabular}{|r|r|r|} \hlinexx & P(x)P(x) & x⋅P(x)x \cdot P(x) \\ \hline 3 & 0.19 & \\ \hline 4 & 0.2 & 0.8 \\ \hline 5 & 0.37 & \\ \hline 6 & 0.24 & 1.44 \\ \hline \end{tabular} μX=4.66\mu_{X}=4.66

Studdy Solution

STEP 1

1. The table provides a probability distribution for a discrete random variable X X .
2. The mean of the probability distribution is denoted by μX \mu_X .

STEP 2

1. Complete the table by calculating the missing values of x⋅P(x) x \cdot P(x) .
2. Compute the mean of the probability distribution using the completed table.

STEP 3

Calculate the missing value for x=3 x = 3 :
x⋅P(x)=3⋅0.19=0.57 x \cdot P(x) = 3 \cdot 0.19 = 0.57

STEP 4

Calculate the missing value for x=5 x = 5 :
x⋅P(x)=5⋅0.37=1.85 x \cdot P(x) = 5 \cdot 0.37 = 1.85

STEP 5

Sum the values of x⋅P(x) x \cdot P(x) to find the mean:
μX=0.57+0.8+1.85+1.44 \mu_X = 0.57 + 0.8 + 1.85 + 1.44

STEP 6

Compute the sum:
μX=4.66 \mu_X = 4.66
The completed table and mean are:
\begin{tabular}{|r|r|r|} \hline x & P(x) & x \cdot P(x) \\ \hline 3 & 0.19 & 0.57 \\ \hline 4 & 0.2 & 0.8 \\ \hline 5 & 0.37 & 1.85 \\ \hline 6 & 0.24 & 1.44 \\ \hline \end{tabular}
The mean of the probability distribution is:
μX=4.66 \mu_X = 4.66

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord