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Hi, please only bid / accept if you are fully able to answer these questions. I need a full explanation so I can fully study the concepts! Please let me know if you need more time or you’d like to be paid more. I’m cautious because I have gotten incorrect explanations before. Thank you so much (:

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(A) c=

(B) c=

1B 3B 3.

(C) c=

(D) c=

(E) c= 1.

5. Let X be a real random variable with cumulative distribution function FX and Y = x2. Then the

cumulative distribution function for Y and y> 0 is given by

[1 Point)

(A) Fy(y) = Fx(y).

(B) Fy(y) = Fx(yº).

(C) Fy(y) = Fx(y).

(D) Fy(y) = Fx(y).

(E) Fy(y) = Fx(y?).

6. Let X be a real random variable and f:R + R the function with

f(0) =

ſ1,

=> 0

-1, x < 0.
Which of the following statements for Y = f(X) is true?
[1 Point]
(A) E[Y] = 0.
(B) E[Y) = 1.
(C) Var[Y] = 2.
(D) Y is a continuous real random variable.
(E) Y = u({-1, 1}).
7. A particle moves randomly to the left or the right in a step-by-step fashion. Its position after the
nth step (n = N) is modelled by Sn = X1 + ... + Xn where X1, X2, ... are i.i.d. random variables
with X1 ~U({-1,1}). Which of the following statements is false?
[1 Point]
(A) The expected position of the particle after n steps (E[Sn]) is 0.
(B) The expected square of the position of the particle after n steps (E[S2]) is n.
(C) Sin converges to zero in probability as n → 00.
(D) For large n, the position of the particle can be approximately described by a N (0,n)-distribution.
(E) For large k e N, the positions of the particle after n resp. n + k steps (Sn resp. Sn+k) are
independent
8. Let a € (0,1). What is the (1 – a)-quantile of a &(1)-distribution, i.e. the value u1-o such that for
2~8(1), we have P(Z
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Tags:
random variables
cumulative distribution
Real random variables
continuous real random variable
step by step fashion
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