Find f(t). e *{! s(s+ 1),

Q: x-1 Given p(x) = (.33)(.67)^', x = 1, 2, 3... %3D Find p(2). O A. .7789 о в. 2211 О с. 33 D. none of…

A: Let X be the random variable having probability mass function is,  P(X) = (0.33)*(0.67)x-1 ,     x =…

Q: Suppose X and Y are r.v.s such that E(X) = 4, Var(X) = 48, E(Y ) = 2, andVar(Y ) = 5. Find upper and…

A: To find the upper and lower bounds for E(XY), we need to use the Cauchy-Schwarz inequality. For any…

Q: Let X - U[10, 30] and A = {x < 15}. 1. P(A) = 2. E(X|A) =

A: Given: X~U10, 30 and A=x≤15

Q: (8) Let X-b(n, p), with E(X) = 6 and var(X) = 4.2, then P(X ≤ 6) = 0.608.

A: here given , E(X) = 6 var(X) = 4.2 for Binomial Distribution  mean = E(X) = np and Variance  = npq

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

A: I am attaching image so that you understand each and every step.

Q: if L(e3t) = then L(S, e34 du) is. S-3

A: Formula:  If Lft=Fs, then L∫0ufudu=Fss. It is given that Le3t=1s-3. By the formula,…

Q: Evaluate L{r'e}. (a-b)! A. aーb+1 (a+b)! В. a+b+1 b! C. (s -n+a) b+1 a! D. (s-b+r)** (ab)! E. ab+1

A:

Q: Show that for all x>0, e* >1+x+÷ 2.

A:

Q: Let S(2) = ) for |z| <1. 1 n=1 zn Evaluate f(10) (0). You may leave factorials in your answer…

A: In the question we are given a complex function f(z) in terms of infinite series, and we have to…

Q: 10.3.7. As usual let D8 g² = e, gf H = = = (a,b | a4 = b² = e, ba f2g). Let G {e} x D8 ≤ G. (a) What…

A: image uploadedExplanation:Step 1: Step 2:Step 3: Step 4:

Q: Suppose X has the following p.m.f. f(x) = cx2, x= - 1,0,1 for a constant c. A. Determine the…

A: For any probability distribution to be valid, the sum of probabilities over the range of the random…

Q: 1. Let X~Poisson(a). Show that E[X(X – 1)(X – 2) ... (X – k)] = ak+1 -

A: Solution

Q: 6. Let f(x) = 20/(x6 + x4 + x² + 1). %3D (a) Show that for any k e [5,20], there is a point c e…

A:

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: If f(x) = then, %3D 1. D; = R R; = {1,0} 2. D, = [1,00) R; = [0, c0) 3. D; = R R; = {1,–1} 4. D; =…

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Q: 6. Find f'(1) if Ax) = nx

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Q: uppose that S is the set of successful students in a classroom, and that F stands for the set of…

A: Given that expression we have to find the value of

Q: 4. If E(R) exists, show that |E(R)| < E(|R]).

A:

Q: Liouville function X(n) is given by formula

A:

Q: tudent  rolls  a  fair,  6sided  die  in  the  morning.  If  he  rolls  a  1,  then  he  does his…

A:

Q: 6. Show that =+ E-(-1)"(n+ 1) E)". when Iz – 2| < 2.

A: Seriese expansion

Q: -3 (k) [ 6* dx

A: SINGLE REQUEST SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 1-2x (c) Determine the values of a, b and c if =1+ax+ bx? + cx. Hence, by 1+2x, 1 show that 2 s 3,…

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Q: Show that e* ≤ 1/(1 − x) when x < 1. [Hint: Consider f(x) = (1 − x)e*.] -

A:

Q: If k(x) = {x + 4 1 - x if x < 0 if 0 sx < 1, find the following. if x 2 1 (a) k(-5) (b) k(0) (c)…

A: We are given a piecewise function k(x) and we need to find the value of the function for different x…

Q: 10. |G/H| [G:H]. *True False

A: 10. True or False: |G/H|=[G:H]

Q: > [2] S 1+e* dx 1-ex

A: The solution is given in the next step.

Q: 10. List the members of H = {x²|x = D₁} and K = {x € D₁ | x² = e}.

A:

Q: 4. S(x + e*)²dx

A: ∫x+ex2dx

Q: Let X~ N(1,4). What is E(X²)?

A: Here, it is given that X~N(1,4) that is X follows Normal distribution with mean μ=1 and variance…

Q: k* for some constant k". Lp.) Show that L(po)

A:

Q: 14. Let f(n) = n² + 20 and g(n) = n³. Show that f(n) is O(g(n)) by finding a positive integer N for…

A:

Q: We know [n] = {1, 2, - . , n}. Let A = [8], B = {x € A : x > 5}, and C = {x € 1 (D

A: Cartesian Product of two sets: A×B denotes the Cartesian product of two non-empty sets A and B. Also…

Q: 3. Prove that eª >1+x for x > -1

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Q: Evaluate the following sums: (i) Σ(k + 1)x*, |x| < 1;

A: ∑k=0∞k+1xk,      x&lt;1 Note: There is three different question, according to the guidelines we are…