Question

In: Statistics and Probability

Do the following using R. You must also turn in a copy of your R code....

Do the following using R. You must also turn in a copy of your R code.

(10) What is the probability a beta (1, 8) random variable is less than 0.13?

(11) What is the probability a beta (3, 9) random variable is greater than .4?

(12) What is the probability a beta (18,4.4) random variable is between 0.6 and 0.7?

(13) At what value of x is the probability that a beta (4, 7) random varable is less than x equal to .71? That is, for what x is P r(beta(4, 7) random variable < x) = .71?

(14) At what value of x is the probability that a beta (12.2, 25.7) random variable is less than x equal to .2? That is, for what x is P r(beta(12.2, 25.7) random variable < x) = .2?

Solutions

Expert Solution

R- Script is

# 10. what is the probability abeta(1,8) random variable is less than 0.13
p10=pbeta(0.13,1,8);p10

#11. what is the probability a beta (3,9) random variable is greater than
p11 =1-pbeta(0.4,3,9);p11

# 12 what is the probability a beta(18,4.4) random variable is between 0.6 and 0.7
p12 =pbeta(0.7,18,4.4)-pbeta(0.6,18,4.4);p12

#Q13 At what value of x is the probability that a beta(4,7) random variable is less than x equal to 0.71
p13 =qbeta(0.71,4,7);p13

#Q14 At what value of x is the probability that a beta (12.2,25.7) random variable is less than x equal to 0.2
p14=qbeta(0.2,12.2,25.7);p14

R-console output is

> # 10. what is the probability abeta(1,8) random variable is less than 0.13
> p10=pbeta(0.13,1,8);p10
[1] 0.6717883
>
>
> #11. what is the probability a beta (3,9) random variable is greater than
> p11 =1-pbeta(0.4,3,9);p11
[1] 0.1189168
>
>
> # 12 what is the probability a beta(18,4.4) random variable is between 0.6 and 0.7
> p12 =pbeta(0.7,18,4.4)-pbeta(0.6,18,4.4);p12
[1] 0.09770375
>
>
> #Q13 At what value of x is the probability that a beta(4,7) random variable is less than x equal to 0.71
> p13 =qbeta(0.71,4,7);p13
[1] 0.438946
>
>
> #Q14 At what value of x is the probability that a beta (12.2,25.7) random variable is less than x equal to 0.2
> p14=qbeta(0.2,12.2,25.7);p14
[1] 0.2572049
>

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