Answer in Statistics and Probability for Pethias Lungo #135942
January 22nd, 2023
Let “X=” number of patients who asked for water: “Xsim Bin(n, p)”
Given “p=3/5=0.6, n=10”
i. “P(X=6)=dbinom{10}{6}(0.6)^6(1-0.6)^{10-6}=0.250822656”
ii. “P(Xleq4)=P(X=0)+P(X=1)+P(X=2)+”
“+P(X=3)+P(X=4)=”
“=0.0001048576+0.001572864+0.010616832+”
“+0.042467328+0.111476736=0.1662386176”
iii. “P(Xgeq4)=1-P(X=0)-P(X=1)-“
“-P(X=2)-P(X=3)=”
“=1-0.0001048576-0.001572864-0.010616832-“
“-0.042467328=0.9452381184”
iv. “E(X)=np=10(0.6)=6”
v. “V(X)=np(1-p)=10(0.6)(1-0.6)=2.4”
“sigma_X=sqrt{2.4}approx1.55”
Let “X=” the execution time of programs: “Xsim Exponential(lambda)”
Given “lambda=5”
i. “P(X<4)=1-e^{-5(4)}approx0.999999998approx1”
ii. “P(X>6)=e^{-5(6)}approx10^{-13}approx0”
