Show that if X ∼ Geom (p) then P(X = n + k | X > n) = P(X=k)  for n, k≥1.

Q: The constant k which satisfies P(k <T < to.2) = 0.3 is: %3D А. -to.2 В. to.1 С. -to.1 D. None of the…

A: t distribution: Let us assume X is a random variable following standard normal distribution and Y is…

Q: a) Let f(x)=−x4−8x3+2x+6. Find the open intervals on which f is concave up (down). Then determine…

A: Given function, f(x)=-x4-8x3+2x+6

Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: HW_2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 < Z < 2) c) p(-2 < Z < 1)

A: Solution

Q: Determine the global extreme values of the f(x, y) = 12x - 2y if y ≥ x − 6, y ≥ −x − 6, y ≤ 6. (Use…

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Q: Let X have a p.d.f. fx(x) = {} -1 < x < 2, otherwise. Find the p.d.f. of Y = X².

A: Given X have a p.d.f and Y=

Q: There are 45 wild hogs in a forest, of which 8 were caught earlier and labeled. Some time later, for…

A: This is a problem of hypergeometric distribution. The hypergeometric distribution models the…

Q: ) Let f(x) = c) 1 x + 3 following: a) ƒ (-3) = = defined, write "undefined". Evaluate the Undefinec…

A: We have given function  fx=1x+3 (a) Put x=-3 f-3=1-3+3=10 f-3=Undefined (b) fx+h=1x+h+3

Q: EN: Find a) zo value if P(Z > zo) = 0.7 b) P(-1.37 < T < 2.36) when v = 10 c) x² if P(x² < X² < 22)…

A: The question is about continuous prob. distributionIntroduction :Std. normal dist. : is a std.…

Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

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Q: 15. Find x so that m || n. (5x – 20)°

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Q: D if x,Y,2 inclepndent Variables and z function in X, Y which achieves the eguation find az…

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Q: At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees…

A: At a company, 20 employees are making contributions for a retirement gift

Q: COSZ 2) if Res(f,x) of the function f(2)=- a) -3/8 b) #-6 2ti c) 1/e d) 8/5 -is

A: To find Resf, π of the function fz=cos zz2 z-π3.

Q: If k = (11.03.-9.12,3.15,-1.01) in R4 then k| = %3D %3D

A: Given  k = 11.03, -9.12, 3.15, -1.01t in R4. We have to find the value of k1.

Q: A. If X~N(196,20), find x such that Pr(X < x) = 0.945.

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Q: 6-2 x and y are independent and uniform in the interval (0, a). Find the p.d.f. of (a) x/y,

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Q: It is given that X~N( 30, 5). Find P(27<X<33)

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Q: 10. Determine f" if f(x) = √√√x³ +2.

A: Given : f(x)=x3+2To Find :f''

Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

A: Apply formula of trapezoidal error

Q: It is given that X~N(30,5). Find P(27<X<33)

A: Given : X~N(30,5)

Q: Let X~ N (24, 49), Find P( 10<X< 38)

A: Given sample are: 24, 49 Mean of these samples are: μ=24+492=36.5 Standard deviation:…

Q: (d) P(X > 7) = i (e) Determinex such that P(X < x) = 0.99. X = i

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Q: Q/ Let X be the r.v such that E (X) = 2 , E(X²) = 2a , E((2+ aX)²) = 2a³ %3D %3D Find the value of a…

A: It is given that, E(X) = 2, E(X2) =2a, E((2+aX)2) =2a3

Q: 5) Evaluate F dr where F(r, y) = ry i + j, , r(t) = ti+ 3t j, 1<t<4 %3D

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Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

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Q: Find the CDF of the distance of two randomly chosen points of the [0,6] interval. F(x) - if x6.

A: Given x~U(0,6)

Q: Given, F = x²yî – 2xzj + 2yzk. Find V × (V × F)

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Q: 7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the…

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Q: What is the largest interval on which the following IVP sure to have a unique solution: (t…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: (d) If each fn has fewer than M discontinuities (where M ∈ N is fixed), thenf has fewer than M…

A: To Show: If each fn has fewer than M discontinuities (where M ∈ N is fixed), then f has fewer than M…