(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 (c) 3 (d) 4 (e) None of these

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: Find (a) The constant K (b) P(X> 1) (c) P(|x|<3)

A: To determine the value of K we will use the fact that the integration of pdf f(x) over whole range…

Q: (7) Suppose that X₁ and X₂ are two random variables with j.m.g. f. 2 (t₁ - 1)(t₂-1) + (t₂ − 1)² '…

A: It is given that the two random variables X1 and X2 has the m.g.f as below: MX1,…

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

A: Formula used: fx=x-2k           1&lt;x&lt;∞0                   Otherwise

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: (1) Let X be a random variable with p.d.f. ke 2x f(x) ={ 0 <x<0 , then o.w (a) k=3 (b) k=2 (c) k =-…

A: Reviewing information, X is a r.v. with pdf, f(x)=k·e-2x                                   ;…

Q: We know that X is an unknown distribution with a mean of u and a variance Xị are i.i.d. e

A: From the given information, X is an unknown distribution with a mean of μ and a variance of σ2; And…

Q: 3. If X and Y are independent uniform (0, 1) random variables, show that 2 for a > 0 (a + 1)(a + 2)…

A: X and Y are independent U(0,1) random variables:Objective: Show that:

Q: Which of the following is equal to Cov (X+ Y, 2X +Y), where X and Y S ? are random variables on a…

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: Suppose X and Y are two independent and identically distributed geometric random rariables. The pmd…

A: PMF of X is given by, P(X=x) = p(1-p)x-1 , x=1,2,3.... Now,  ⇒P(X≥x)= ∑t=x∞ P(X=t)= ∑t=x∞p(1-p)t-1 =…

Q: (40) Let X be a random variable with p.d.f. (k +4)e¯3x f(x) ={ 01) O.w

A: a)Use the condition of valid pdf to find the value of k…

Q: (3) Let X be a random variable with p.d.f -(3x+6) 15 0<x<1 f(x) =- then E(Gx) is O.w 4 7 15 (b) 15…

A: We want to find correct answer for question

Q: 1-4x 10) If a random variable assumes 4 values with probability 1+3x 1-x 1+2x and ¹-4 4 4 4 the…

A: Here for given probability check whether using value of x total probability is equal to 1 and all…

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

A:

Q: (1) E(E(X)) = E(X) (2) E(X – E(X)) = 0 (3) Var(X) = E(X²) – [E(X)]² (4) Given constants a and b,…

A: Discrete random variable is defined as a variable which can take only specific values. For example…

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

A:

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: (5) Let X be a random variable with p.d.f. k 1<x<o 2 f(x) =< , find k. O.w

A: Given: fx=kx2            1&lt;x&lt;∞0                 Otherwise

Q: 6x) 0<x<1 S(x)%=D , then p(x<1) is (a) 1 (b) 2 (c) 3 (d) 4 (c) None of these

A: It is an important part of statistics. It is widely used.

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

A: Given, X is a random variable with the function below

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: 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 has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)?…

A: PGF of a Random Variable is given by, Gx(t) = Σ tx P(X=x)

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: (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:

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!