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Math 380 Questions with complete solution 2025/2026

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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

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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)

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