(4) Let X be a random variable with p.d.f. 2e-2x 0

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: (17) Let X be a random variable with p.d.f. o >x>0 f(x)=< find E(e) O.w

A: Solution : Given :  f(x) = 15e-15x          0&lt;x&lt;∞0           o.w Here X ~exp(15) M.G.F of x is…

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

A:

Q: 2. A random variable X has pdf |x| < 1 elsewhere. cx(1+ x) a. Find c. b. Find E{X}and V AR{X} c.…

A:

Q: 3. Let X be a random variable that is equal to the number of times a six-sided die lands on 6 over…

A: Possible outcomes for :- X=0 : No sixes in two rolls.- X=1 : One six in two rolls.- X=2 : Two sixes…

Q: 7. Let M(t)=(1/6)et +(2/6)e²t+(3/6)e³t (Moment generating function of X) a. Find E(x) b. Find…

A:

Q: 2. Let X be a random variable with E[X] = 15 and Var[X] = 10. Suppose Y = 2X – 7, Use the properties…

A: Given,E(X)=15Var(X)=10and Y=2X-7

Q: Let X be a random variable with p.d.f f(x) = 2x,0 < x < 1. Find E(Vx) 2/3 5/4 3/2 O 4/5

A:

Q: (51) Let X be a random variable with p.d.f. 2e-2x 0<x<00 = (x) , find E(e") O.w

A:

Q: Let X be a random variable with p.d.f. x = 1,2,3 f(x) = { find (1) k (2) E(x²) O.W

A: Solution: 36. From the given information, the probability density function of X is

Q: 20) Let X be a random variable with p.d.f. k T<x<10 f(x) =- , find k. O.w

A: Solution: Let X be the random variable with pdf f(x) is  f(x)=kx       1&lt;x&lt;100      otherwise

Q: Let X be a random variable with p.d.f. {(k + 1)e¬8: f(x) = 0<x<0 , find (1) k (2) P(x< 1) O.w

A: Solution: 39. From the given information, the probability density function of X is

Q: Suppose X is a continuous random variable with p.d.f. fX(x) = kx2(1 − x) if 0 < x < 1. (b) Find the…

A:

Q: (b) A continuous p.d.f for a random variable X with function, P(x) = SX for 01|x< 4).

A:

Q: E e-2*)

A: Let X be the random variable with p.d.f f(x)=2l-2x       ; 0&lt;x&lt;∞0               ; otherwiseNow…

Q: Let X be a positive random variable; i.e P(X ≤ 0) = 0. Which one is correct? (1) E (+) (²) (11)…

A: Given:X is a positive random variable, meaning .We need to determine which of the statements is…

Q: (45) Let X be a random variable with p.d.f. ((k +4)(x+2) 0 <x<2 f(x)=- find (1) k (2) E(x) O.W

A:

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: Let X be a random variable with p.d.f. 2e-2x f(x)=< 0<x<0 , find E(e2") O.w

A: Let  X be a random variable with the pdf  fx=2e-2x                 0&lt;x&lt;∞0…

Q: (52) Let X be a random variable with p.d.f. 1 0<x<0 f(x) = ,find E(e") O.w -in

A:

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: (7) Let X be a random variable with p.d.f. 1<x<0 f(x) = { ,find k. O.W

A: Reviewing information, X is a r.v. with pdf,f(x)=kx-2                          1&lt;x&lt;∞0…

Q: For a random variable X, you are given: E[2*] = e#(z-1) Determine the coefficient of variation of X.

A:

Q: The distribution function of the random variable X isgiven byF(x) = 1 − (1 + x)e−x for x &gt; 00 for…

A: The required probabilities are as follows:

Q: (34) Let X be a random variable with p.d.f. x= 1,2,3 f(x) ={ , find (1) k (2) E(²) O.w

A: X is a random variable with pdf: The sum is always 1. So,

Q: (22) Let X be a random variable with p.d.f. 3k e 0<x<0 S(x) = find k. O.w

A:

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

A: Solution: 32. From the given information, the probability density function of X is

Q: A continuous random variable X has p.d.f. 5x-6, for x > 1 f(x) = 0, Suppose Y = . (a) Determine the…

A: Given thatSuppose

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!