if X is positive integer
f(x) = (4/X)f(x-1), for x=1,2,3...
what is pdf
if X is positive integer f(x) = (4/X)f(x-1), for x=1,2,3... what is pdf
. 3. For each positive integer k, consider Xt as a continuous random variable with PDF given by focsi=fksk-! 065:-1, . kolo, otherwise. Let W denote the number of k=1,2,..., 12 for which X = 23. Calculate <WY ..
4. For the random variable X with the pdf f(x) = 1 defined on [0,1]: a. Obtain the pdf and cdf for the transformation Y=-2lnX b. P(Y > e) =?
9.A discrete random variable X has pdf of form f(x) x-1,2, ...n, and zero otherwise. A) Find c. B) Find an expression for f (x). 10. If f(x) Cx for x 1,2,3, ... pq*-1 otherwise Find an expression for F(x). Show your work! 9.A discrete random variable X has pdf of form f(x) x-1,2, ...n, and zero otherwise. A) Find c. B) Find an expression for f (x). 10. If f(x) Cx for x 1,2,3, ... pq*-1 otherwise Find an...
20 -{24R/1<x<1+ }}-(1,1+ 4) for each positive integer S: = ? a. US = ? i=1 4 b. O S = ? 11 c. Are S1, S2, S3, ... mutually disjoint? Explain. d. ÜS; = ? =1 72 e. n S = ? 1-1 00 f. US = ? 00 g. S; = ?
4. Let X have pdf f (x) as follows f(x) = 1.8 1(0 1/21+ .21(1/2 < x 1) x (8 pts) What is E[X]? Justify your answer. . (12 pts) Write Matlab or pseudocode that will produce 10, 000 PRNG samples with the dis- tribution of X. Have the output recorded in the vector a (i.e., so that ar(1) is the first sample, r(2) is the second sample, etc.) 4. Let X have pdf f (x) as follows f(x) =...
For an integer n > 0, consider the positive integer F. = 22 +1. (a) Use induction to prove that F. ends in digit 7 whenever n 2 is an integer (b) Use induction to prove that F= 2 + IT- Fholds for all neN. (c) Use (b) to prove that ged(F, F.) = 1 holds for all distinct nonnegative integers m, na (d) Use (e) to give a quick proof that there must be infinitely many primes! That is...
Let n be a positive integer and let F = {X 5 [n]: X|2|[n] \X]} Prove that F is a maximum intersecting family.
Let f be the pdf on a continuous random variable Z. The variance ofZ is given by σZ and the pdf is symmetric (f(x) = f(−x)) and everywhere positive.Define another random variable X as X = α3Z3 + α2Z2 + α1Z + α0.(i) For which values of αi are X and Z uncorrelated?(ii) For which values of αi are X and Z independent?
7. A probability density function (PDF) is given by: f(x)-21x3 for x>a What value of 'a' will make this a PDF? 8. A probability density function (PDF) is given by: f(x) k(8x-x2) for 0<x<8 What value of 'k' will make this a PDF? 9. A probability density function (PDF) is given by: f(x)-e.(x4) for x> a What value of a will make this a PDF? 10. A probability density function (PDF) is given by: f(x)-15x2 for-a<x<a What value of a...
lan 5 15 The pdf of x is f(x) = 0.1, 3<x< 13. Find the 60th percentile. (the answer is an integer)