Math 380 Questions with complete
solution 2025/2026
Geometric Distribution - correct answer ✔Density Function:(1-p)^(x-1)p
Cumulative Distribution:(1-q)^x
Moment Generating:(pe^t)/(1-qe^t)
E[x]= 1/p
Var[x]=q/p^2
Binomial Distribution - correct answer ✔Density Function: (n)p^(x)(1-p)^(n-x)
(x)
Moment Generating Function:(q+pe^(t))^(n)
E[x]= np
Var[x]= npq
Negative Binomial Distribution - correct answer ✔Density Function:(x-1) (1-p)^(x-r)p^(r)
(r-1)
Moment Generating Function:
(pe^(t))^(r)/(1-qe^(t))^r
E[x] = r/p
Var(x) = rq/p^(2)
solution 2025/2026
Geometric Distribution - correct answer ✔Density Function:(1-p)^(x-1)p
Cumulative Distribution:(1-q)^x
Moment Generating:(pe^t)/(1-qe^t)
E[x]= 1/p
Var[x]=q/p^2
Binomial Distribution - correct answer ✔Density Function: (n)p^(x)(1-p)^(n-x)
(x)
Moment Generating Function:(q+pe^(t))^(n)
E[x]= np
Var[x]= npq
Negative Binomial Distribution - correct answer ✔Density Function:(x-1) (1-p)^(x-r)p^(r)
(r-1)
Moment Generating Function:
(pe^(t))^(r)/(1-qe^(t))^r
E[x] = r/p
Var(x) = rq/p^(2)
