Answer to Question #293560 in Statistics and Probability for Maria

Question #293560

Construct a probability distribution of the random variable X for


the number of false answers in a 4-item true or false test.

1
Expert's answer
2022-02-03T18:09:51-0500

Solution:

X = the number of false answers

X = {0,1,2,3,4}

"p=q=\\frac 12,n=4"

"P(X=0)=^4C_0(\\frac 12)^0(\\frac 12)^4=\\frac 1{16}\n\\\\P(X=1)=^4C_1(\\frac 12)^1(\\frac 12)^3=\\frac 4{16}=\\frac 14\n\\\\ P(X=2)=^4C_2(\\frac 12)^2(\\frac 12)^2=\\frac 6{16}=\\frac 38\n\\\\ P(X=3)=^4C_3(\\frac 12)^3(\\frac 12)^1=\\frac 4{16}=\\frac 14\n\\\\P(X=4)=^4C_4(\\frac 12)^4(\\frac 12)^0=\\frac 1{16}"

Thus, probability distribution of X is:

X P(X)

0 1/16

1 1/4

2 3/8

3 1/4

4 1/16


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