(1) Let X be a random variable with a function 3 1 x = 0,1, 2,3 4 x! (3—х)! f(x) =- , then E(x)is O.W 5 (b) 3 7 17 (c) 3 (d) (e) None of these | 2 2 27

Q: (37) Let X be a random variable with p.d.f. (x+1)e2* x=1,2,3 f(x) =- , find (1) k (2) E(x² +1) O.w

A: The probability distribution table is obtained as :  x 1 2 3 f(x) 2e2k 3e2k 42k Every…

Q: Example 4.1.12 X is a discrete random variable with pmf f (x) given by f(x) = kq* x= 0, 1, 2, . , 0…

A: Answer: Using the given data,

Q: 7.3.3. Random variables X and Y have joint PDF ( be-(2r+»w) z20, y 2 0, fx.x (2, y) - otherwise. Let…

A: Given : fx,yx,y = 6e-2x+3y   x≥0 , y≥00                    otherwise

Q: (4) If X and Y are two random variables, the joint moments can be derived from the joint…

A:

Q: if X is poisson random variable with A=2 then E(x+4) 3D O none 6. 0 4 0 5 O 2 O O O 0 0

A: Given that X is a poisson random variable with λ=2 then we have to find E(X+4)so for the required…

Q: (1) Let X be a random variable with a function [3 |4 х! (3— х)! 1 x = 0,1, 2,3 f(x) = { then E(x) is…

A: Solution: 1. From the given information, the probability function of a random variable X is

Q: 2- Suppose that (a) 8/3 a is a joint probability mass function of two random variables X and Y. Then…

A:

Q: 1. X and Y are independent if fx\y(¤ | y) = fy(y). 2. min(X, Y) are considered as function of random…

A: We have given that the statements related to two random variables X and Y. Here, need to find out…

Q: 14- If the p. d. f of a random variable X is f(x) = 1,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is (a) 0.5833…

A:

Q: If a random variable X is defined such that: E[(X - 3)2] = 18 and E[(X-1)²] = 34. Then the values of…

A:

Q: 5. X and Y are two discrete random variables. If the covariance between X and Y is positive, then:…

A:

Q: Let X be a random variable with p.d.f f(x) = c+ 1.2x2,0<x< 1. Find a constant c if E(X) = ! 0.6 0.4…

A:

Q: 2. Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as…

A: a) (i) Value of k: The value of k is obtained as follows: (ii) E(X): The value of E(X) is computed…

Q: 14- If the p. d. f of a random variable X is f(x) = 1,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is (a) 0.5833…

A:

Q: 7) Let X a random variable with pmf P(X = x|N) =*= 1,2,..N, and let Y = 2X +1, where a, be R then EY…

A: The pmf of X is PX=x|N=1N The expectation of X is given by…

Q: (1) Let X be a random variable with a function 3 1 x = 0,1, 2,3 4 х! (3—х)! f(x) = then E(x) is o.w…

A: Let X be a random variable with a function, f(x)=341x!(3-x)!                      ;x=0,1,2,30…

Q: If a random variable X is defined such that: E[(X- 3)2] = 18 and E[(X- 1)'] = 34. Then the values of…

A: answer is given below

Q: Theorem 7-10. If X is a random variable which assumes only integral values with probability…

A:

Q: (3) Let X be a random variable with p.d.f E(3x+6) 15 f(x) =. 0<x<1 , then P(0 <x < 0.5) is O.w

A: (3) The pdf is, fx=2153x+6        0&lt;x&lt;10                         o.w

Q: If a random variable X is defined such that: E[(X – 3)²] = 18 and E[(X – 1)²] = 34. Then the values…

A:

Q: (2) Let X be a random variable with a function 3 1 x = 0,1, 2,3 4 x! (3- x)! f(x) =- then p(x>2) is…

A: We are provided with the PMF of a random variable X. Now we know that, PMF of a discrete random…

Q: (13) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) ={ , find E(e2*) O.W

A: Solution :  Given :  f(x) = 2e-2x    0&lt;x&lt;∞0   o.w     E( e-2x )  = ∫x e-2xf(x) dx…

Q: (2) Let X be a random variable with p.d.f. (k 1<x<10 S(x) = , then (a) k-2 (b) k-8 (c) k- (d) k-3…

A: according to our guidelines we can answer only  first question and rest can be re posted.

Q: (1) Let X be a random variable with a function (3 1 4 xt (3-x)! *- 0,1, 2,3 , then E(x+1) is o.w (e)…

A:

Q: -. Determine the constant c so that f(x)=cx, x=1, 2, 3,...,10 satisfies the conditions of being a p.…

A: The given probability distribution can be desctibed as X 1 2 3 4 5 6 7 8 9 10 f(x) c 2c 3c 4c…

Q: X and Y are independent random variables. Determine E[Z], where Z=X+Y. o 1 2 3 4 Px(x) 1/8 3/16 3/8…

A: E(X)=∑ixP(X)E(X)=0×1/8+1×3/16+2×3/8+3×3/16+4×1/8E(X)=0+316+68+916+48E(X)=2…

Q: 4. Suppose X and Y are independent random variables such that E(X) = 0, 6, E(Y) = -1, Var(X) = 1,…

A: 4. The given value are EX=0,EY=-1,VarX=1,andVarY=4.

Q: 14- If the p. d. f of a random variable X is f(x) = 2,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is (a) 0.5833…

A:

Q: (1) Let X be a random variable with a function [3 4 x!(3-x)! S(x) = { 1 x = 0,1, 2,3 , then E(x)is…

A: Solution: Note: Hello! As you have posted 2 different questions, we are answering the first question…

Q: (41) Let X be a random variable with p.d.f. [(k+4) 0<x<5 ,find (1) k (2) E(x +1) (x) O.w

A: Given information: X is random variable with probability density function. f(x)=k+4; 0&lt;x&lt;50…

Q: 17.1 The probability of an event depends on the random variable X and can be expressed by the…

A:

Q: (1) If a random variable X is a constant, i.e.., X =a then E[a]= a, where a is a constant.

A:

Q: (2) Let X be a random variable with p.d.f (3x² +6x) [>x>0 S(x) =- , then p(x < 1) is O.W (a) 1 (b) 2…

A:

Q: (1) Let X be a random variable with p.d.f. 1 -8x 0<x<0 k f(x) = find k. O.w

A:

Q: 4. If X is a binomial random variable with parameters p = 0.6 and n = 4, then P(X = 2) equals O…

A: Given,n=4p=06X~Binomial(p=0.6 , n=4)P(X=x)=nx px(1-p)n-x    ;  x=0,1,2,.....n

Q: (24) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) =- , find E(e³*) O.w

A: Here,Ee5x=∫0∞e5xfxdx=∫0∞e5x2e-2xdx=2∫0∞e3xdx=2e3x30∞=23e3x0∞=23e3∞-e30=23∞-1=∞

Q: a.b.c

A: Standard normal distribution:The standard normal distribution is a special case of normal…

Q: Random variables X and Y have a joint PMF described by the following table. y = -1 y = 0 y = 1 1/16…

A: Probability density function explain the probability occurrence of all the observations in a…

Q: 2. Let X be a random variable with p.m.f., (1+x? 20X = -1,0,1,2,3 0 ,otherwise. f(x) = Find E(3X² +…

A: Given function isf(x)={1+x220,    x=-1,0,1,2,30         ,   otherwise

Q: (2) Let X be a random variable with p.d.f. 1<x<10 f(x) =- then O.w (c) k - (d) k-3 (a) k=2 (b) k=8…

A: f(X) = k/x    ;   1 &lt; x &lt;10

Q: 4. Suppose X and Y are independent random variables such that E(X)= 0, E(Y)= -1, Var(X)= 1, and V…

A:

Q: If a random variable X is defined such that: E[(X - 3)2] = 18 and E[(X+1)²] = 34. Then the values of…

A: Variance(X)=E[(x-mu)2].

Q: Example 2.8 The PMF of the number N of customers that arrive at a local li- brary within a one-hour…

A:

Q: If a random variable X is defined such that: E[(X - 2)²] = 18 and E[(X+ 1)'] = 33. Then the values…

A:

Q: (1) Let X be a random variable with p.d.f. ke 0<x<0 Sx) = ,then O.w (b) k - (e) k- (a) k-1 (c) k (d)…

A: According to our guidelines we can answer only first question and rest can be re posted.

Q: (24) Let X be a random variable with p.d.f. 2e-2x 0<x<00 f(x) = find E(e*) O.W

A: Given,f(x)=2e-2x   ;0&lt;x&lt;∞0           ;o.w

Q: Let X and X1, X2, ... be random variables. Then |Xn – X| 1+|X, – X| X, 4 X as n →∞ → E 0 as n → 0.

A: Solution: From the given information, X and X1, X2 …be random variables.

Q: (1) Let X be a random variable with p.d.f. ke f(x) = { 0<x<00 , then O.w (b) k =? (c) k = (d) k=5…

A:

Q: (3) Let X be a random variable with p.d.f 2(3x+6) 0<x<1 15 f(x) =- , then P(0<x<0.5) is O.w

A:

Q: (20) Let X be a random variable with p.d.f. 2 1 3 e -- 0<x<∞ k f (x) = find k. O.W

A: Given,f(x)=1k e-23x       0&lt;x&lt;∞

Q: (31) Let X be a random variable with p.d.f. x= 1,2,3 x! f(x) ={ , find (1) k (2) E(x) O.w

A:

Q: Example 2.8. Suppose X is a random variable whose CDF is: Fx(1) = lp.1.100 (x) +100.00)(2) +200,500)…

A: C,

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!