Questions asked
Willis James
Numerade educator
Let X ~ Bin(N, p), that is its pmf is f_X(x) = { _N C_x p^x(1 - p)^{N-x} for x ? {0, 1, 2, ..., N} 0 else } It was shown in class E[X] = Np. Calculate Var[X]. (Hint: First calculate E[X(X - 1)])
Nick Johnson
Calculate the expected value and variance for the rv whose pdf is given below. f_L(l) = e^{-l} / (1 + e^{-l})^2 for l ? ?
William Semus
( int_{1}^{infty} ln (u-1) d u )
Mengchun Cai
Problem 2: Let X follow Normal distribution with mean (mu) and variance (sigma^{2}), the form of whose pdf is, [ f_X(x)=frac{1}{sqrt{2pi},sigma}e^{-frac{(x-mu)^2}{2sigma^2}} ] Define the new rv, Y= e^{X}. Work out the pdf (i.e. the distribution) of Y. - 2 pts
Problem 1: Let U follow a uniform rv on the interval [0, 1], the form of whose pdf is, f_U(u) = 1_{[0,1]}(u) = { 1 for u ? [0,1], 0 else Define the new rv, L, as follows, L = ln (U / (1 - U)) Work out the pdf (i.e. the distribution) of L.
Problem 2: Let \( Y \) be continuous \( r v, Y \) is said to follow an exponential distribution with rate parameter \( \lambda \) (denoted \( Y \sim \operatorname{Exp}(\lambda) \) ) if its \( p d f \) is of the form below. \[ f_{Y}(y)=\left\{\begin{array}{ccc} \lambda e^{-\lambda y} & \text { for } y \in \mathbb{R}^{+} \cup(0), & \lambda \in \mathbb{R}^{+} \\ 0 & \text { else } \end{array}\right. \] Given the event \( A=(Y>f) \), work out the conditional pdf of \( M A,-2 \) pts
Breanna Ollech
Problem 2: Let Y be continuous rv. Y is said to follow an exponential distribution with rate parameter ? (denoted Y ~ Exp(?)) if its pdf is of the form below. f_Y(y) = {?e^{-?y} for y ? ?+ ? {0}, ? ? ?+ 0 else} Given the event A = (Y > t), work out the conditional pdf of Y|A.
Problem 1: Suppose ( X sim operatorname{Norm}(mu, sigma^{2}) ), calculate the following: a) ( E[X^{2}] ) b) ( E[(X-mu)^{3}] ) c) ( E[X^{3}] )
Calculate the expected value and variance for the rv whose pdf is given below. f_{Y}(y)=left{egin{array}{ccc}lambda e^{-lambda y} & for y in mathbb{R}^{+} cup{0}, & lambda in mathbb{R}^{+} \ 0 & elseend{array} ight.
