# Do the following using R. You

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

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

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

(12) What is the probability a beta (18,4.4) random variable isbetween 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 isP 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 whatx is P r(beta(12.2, 25.7) random variable < x) = .2?

Answer:

**R- Script is**

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

#11. what is the probability a beta (3,9) random variable isgreater thanp11 =1-pbeta(0.4,3,9);p11

# 12 what is the probability a beta(18,4.4) random variable isbetween 0.6 and 0.7p12 =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 0.71p13 =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 0.2p14=qbeta(0.2,12.2,25.7);p14

**R-console output is**

> # 10. what is the probability abeta(1,8) random variable isless than 0.13> p10=pbeta(0.13,1,8);p10[1] 0.6717883>>> #11. what is the probability a beta (3,9) random variable isgreater than> p11 =1-pbeta(0.4,3,9);p11[1] 0.1189168>>> # 12 what is the probability a beta(18,4.4) random variable isbetween 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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