What is the probability that, out of the 4 balls drawn, exactly 2 are white? . Let the pmf of X be defined by Pr(X= x) = 1 6 ²2=1,2,3,... Show that E(X) = ∞ and thus, does not exist. 9. Given E(X + 4) = 10 (a) E(X²) and E[(X + 4)2] = 116, determine (b) V(X + 4)

Q: Q7 Assuming y = f(x), compute [3xy²] dx

A: The function is y=3xy2.To find : Compute ddx3xy2

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: 7 3 Suppose that f and g are continuous and that f(x)dx = - 3 and g(x)dx = 9. Find (g(x) - f(x)] dx.…

A: Given: ∫37f(x)dx=-3 ; ∫37g(x)dx=9To find the value of ∫37 g(x)-f(x) dx=?

Q: The fixed point/s of the function g(x) = In(e²* – 3e* +3) + x on [0,1] is / are: Select one: а. О, 1…

A:

Q: Find g" (1) for g (x) = xª – x³ + 2x -

A: Topic: differentiation

Q: - Let T : Pn → Pn-1 be T(p) = dr. Find its range and dx nullspace (with explanations) and hence its…

A: Dear students as per our guidelines we can answer only first question. Kindly resubmit the remaining…

Q: 4. Let S = {-1,0,2,4,7}. Find f(S) if а. f(x) — 1 b. f(x) = 2x +1 %3D c. f(x) = |*/s] d. f(x) = [x*…

A: Given:S={-1,0,2,4,7}

Q: Let X have a p.d. f.f(x) that is positive at x = -1,0,1 and zero elsewhere. (a) If f(0) =, find…

A:

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 f(x)=x² - x, xeR then f(f(f(v2))) is: -34 + V2. b. 2/2 +34. c. 34+2/2. d. 34– 2/2. e. 2/2 -…

A:

Q: 18. Let f(x)=2- |2x - 1. Show that there is no value of e such that f(3) -f(0) = f'(c)(3-0). Why…

A: We have given that f(x)=2-|2x-1|for x>12f(x)=2-(2x-1)=-2x+3f'(x)=-2for…

Q: Let f(x) = x2 + ax +b; where a,b ER and f(-)= -1 is an extreme value of f on [0,1], then the values…

A: To Determine: find the values of a and b Given:  Let f(x)=x2+ax+b;  a,b∈ℝ  and f12 =-1 is an extreme…

Q: 4

A:

Q: 2 Let ƒ(x)=x³, g(x)=x³. If it holds (fog)(x)= (gof)(x)?

A:

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

A: Solution

Q: Linearize x³ + ln x about x=3

A: Let f(x)=x3+ln x about x=3 f'(x)=3x2+1x Recall: Linearization  L(x)=f(a)+f'(a)(x-a)  we have a=3

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: 1. Linearize x³ + ln x about x=3 In

A: Given: Linearize x3+ln x about x=3 To find: To find the linearization of x3+ln x about the point x=3…

Q: Let f(x)= x², g(x)= 2x+5, and h(x)=x² –1. Find each. 9. h[S(-2)]= 10. S[g(x-1)] =, 11.

A:

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

A:

Q: (–1)" >) Given: In(1 + x) = if x < 1. n + 1 n=0 2. Evaluate f(2022) (0).

A:

Q: Prove using the e-8 notation that the following functions are continuous at p= 1: (a) g2(r) = 2=+7…

A: ε-δ notation for continuity. Let f(x) be a function defined from ℝ→ℝ. Then, f(x) is said to be…

Q: Pls helpp ASAP

A: To find  h(x)=f(x)*g(x)

Q: Let {X} be i.i.d. such that X₁~ Pa(4, 1500) and suppose that N(2) ~ Po(100). Find E[S(4)] and…

A: Given that  be iid. such that  and

Q: 1. Let f(x) = 12 + 22 + 32 + .+x². Show f(x) is 0(x³).

A:

Q: Let S={0,8,10,−9,−2}S={0,8,10,−9,−2}. Find f(S)f(S) in each of the following cases. a) If…

A: If f is a function from A to B and C be any subset of A. Then f(A)={f(y) : y is an element of A}

Q: If f(x, y) = x²ye*xy, find fx and fyx.

A: Given function is

Q: y 5 4 f(x) 3 g(x) 2 2 3 4 -1 1. 1.

A:

Q: Find the c in the MVT for f(x) = 5x-x2 , 1< x < 5. You might recall the MVT says that there is a c…

A: Consider the provided function, fx=5x-x2,1≤x≤5 Apply the mean value theorem. f'c=f5-f15-1.  Find the…

Q: ind g(-)

A: Given that : The function is g(x) = 2x .

Q: Let g(x) = x- 3. Find f(x) so that h(x) = (f o g)(x). h(x) = Vx- 3 +4 f(x) =O %3D

A: The given functiong(x)=x-3 and h(x)=x-3+4

Q: Q2. Given that f(x) = |6 – 2x|. Draw the graph of f (x) and hence evaluate f f(x)dx. [ Fig 1

A: Let's find.

Q: Convolution. Find the convolution of (a) Πα * Πα. (b) f(x) * ƒ(x), where ƒ(x) = e¯\ª\, -∞< ï<∞.

A: As per the question we are given two functions as: Πa(x) : the rectangular pulse function with…