A continuous random variable X is defined by f ( x ) = (3+x)^2/16 ; -3

Q: X is binomial distribution(n,p), Prove: E(X^2)=E(X(X-1))+E(X)

A: We have given that  X~B( n, p ). The pmf of Binomial distribution is, P( X=x ) = nCx*px(1-p)n-x  So,…

Q: Give the derivation of the variance for the binomial distribution.

A: X~Bin(n,p)

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let X₁, X₂ be IID with \Exp(1), the standard exponential distribution. Show that Z = X₁/X₂ has an…

A: Let X1 , X2  be the iid random variable having exp(1) Then show that Z=X1/X2 has F distribution…

Q: The random variable X ( N (u,5^2)and P(X < 23)= 0.9192. (a)  Find the value of u . (b)  Find the…

A: Given, σ=5 P(X &lt; 23)= 0.9192Mean(u)=?

Q: Suppose that the random variables X and Y have the following joint probability density functio f(x,…

A: f(x,y)=ce-8x-5y ; 0&lt; y&lt;x

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.