Random variable X={A, B, C, D} with p.m.f. {1/4, 1/4, 1/4, 1/4}, calculate its entropy.
Random variable X={A, B, C, D} with p.m.f. {1/2, 1/4, 1/8, 1/8}, calculate its entropy.
Give an example of a discrete or continuous random variable X (by giving the p.m.f. or p.d.f.) whose cumulative distribution function F(x) satisfies F(n)=1-1/n! Thank you very much! Exercise 3.40. Give an example of a discrete or continuous random variable X p.d.f.) whose the cumulative distribution function F(x) (by giving the p.m.f satisfies F(n)1 - i for each positive integer n or
Let random variable X be distributed according to the p.m.f P(a) 0.3 0.5 0.2 · If Y = 2x, what are ELY Var(Y) If Z = aX + b has E121 = 0 and Var(Z) = 1, what are: .
Let random variable X be distributed according to the p.m.f P( 0.3 0.5 0.2 · If Y=2X, what are li E r Var(Y) . If Z = aX + b has EZj-0 and Var(Z)-1, what are: lal
1. Consider sequence of independent identically distributed binary random variable x,,x,,x,,x,-4 , wherepEPr(X:-)-0.7 and Pr(X, =0).1-p=0.3. a) (10 pts.) Complete the table where k denotes the number of 1's in the n! sequence, andkkn-k b) (10 pts.) Calculate H(X) c) (10 pts.) Assume that Pr[T)]21-ε 0.9. Find the corresponding typical sequence set n) d) (10 pts.) Assume Pr[ 21-820.9. Find the corresponding smallest set B ). 2. Consider a random walk random variable X, on the graph in Figure 1....
Consider the discrete random variables X and Y with the following joint p.m.f. Pxr(r,y) 1 0.03 0.100.09 0.08 2 0.050.280.07 0.10 3 0.02 0.120.04 0.02 Find the marginal p.m.F. of X P1 4 Find the marginal p.m.f. of Y Find the conditional p.m.F. of X given Y 3 Find the conditional p.m.f. of X given Y 3. Pae) 2 3 4 . Find the conditional p.m.f. of Y given X 3 .1 . Find the following probabilities Check
Let X be a random variable which follows truncated binomial distribution with the following p.m.f. P(X=x) =((n|x)(p^x)(1−p)^(n−x))/(1−(1−p)^n), if x= 1,2,3,···,n. •Find the moment generating function (m.g.f.) and the probability generating function(p.g.f.). •From the m.g.f./p.g.f., and/ or otherwise, obtain the mean and variance. Show all the necessary steps for full credit.
Let X be a Poisson random variable with parameter λ = 6, and let Y = min(X, 12). (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y? (e) Compute E[Y ].
1. What is the minimum value of the entropy H(X) of a random variable X with an alphabet size M. What is the pmf that achieves this minimum value.
5. Let X be a Poisson random variable with parameter λ = 6, and let Y = min(X, 12). (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y? (e) Compute EY