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

Q: Let X x b(n,-) and E(3x) = E(3-5.x) find n.

A: Given X ~ B(n, 12) P(X=x)=Cxn px (1-p)n-x; x=0,1,....n…

Q: a) Differentiate the function Q(p) = -2³√/p³ (²-P). b) Hence or otherwise, determine Q'(1).

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Q: 1. If f(x) is a function such that f(1) = 2, f(n + 1) = (3f(n)+1)/3 for n = 1, 2, 3, ..., what is…

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Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: c) Let S= {-1, 0, 2, 4, 7}. Find f (S) if i. f(x)=[x/5]. ii. f (x) =L (x² + 1)/3 %3D %3D

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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…

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Q: Let X = n(µ,4) and Var(2x) = E(4–7x) find µ.

A: Given: X ~ N (μ,4) So, V [X] = 4 V [2X] = E [4 - 7X]

Q: 4. Let f(x)= |x| and g(x) = x-3. (a) Determine the formulas for each of the related composite…

A: The composite function is defined as when the output of one function is used as the input of another…

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

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Q: Graph the function h: Z→Z, defined by h(x)=| 3

A: Graph of the function

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…

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Q: 19. Let ƒ(x) = x/(x-2). Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

A: Given,

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: f(2) = e=².

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Q: Using a calculator or computer, sketch the graph of f for k = 1/9, 1/6, 1/3, 1/2, 1, 2, 4. Describe…

A: Given:     f(x) = e5x - kx    k = 1/9 , 1/6 , 1/3 , 1/2 , 1 , 2 , 4

Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

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Q: 3/(a) Let X × b(n, –) and E(x)= E(16–7x) find n.

A: Solution : Given : X ~ b( n, 14 )             E(x) = E( 16-7x ) To find n : It is known that for…

Q: Define a function g(x) of a random 1; if x2x, 0; otherwise variables by g(x) = %3D Where x, is a…

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Q: (a) Е(X), (Ь) var (X), (c) P(-2 <x < 0.5),

A: Let ,  The pdf of X is given by , = 0 ; otherwise Our aim is to find the following : a) E(X) b)…

Q: Show that E[Var(Y |X)] ≤ Var(Y )

A: Show that E[Var(Y |X)] ≤ Var(Y )