2 The random variable X- Po(45). Use a suitable approximation to estimate: a P(X< 40) b P(X> 50) e P(43 < X<52)

Q: Two random variables have expected values E[X] = 0.6 and E[Y] = 0.2 and E[XY] = 1.2. Are X and Y…

A:

Q: Q1\A/ Consider a discrete random variable X whose pmf is given by: Find: 1-E[ X ] and Var( X )? f(x)…

A: Given p.m.f. is  f(x)=13                    x=-1,0,1     =0                        otherwise

Q: A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1…

A: Given: Let X be a Poisson random variable. The probability mass function is provided as:…

Q: The continuous random variable X is uniformly distributed over the interval (2.5, 3.5] a) Calculate…

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Q: Suppose that X and Y are random variables where the conditional expected value of Y given X is given…

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Q: 2. Let X1 and X, be independent random variables with mean u and variance o?. Suppose that we have…

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Q: Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln square root(X)]…

A: The Jensen's inequality is defined as: If p(x) is a convex function then E[p(x)]≥p[E(x)]. Also, a…

Q: Let the random variables X1 and X2 denote the length and width, respectively, of a manufactured…

A: Given: Mean of X1 =EX1=2 Standard deviation of X1 =SdX1=0.2 Mean of X2 =EX2=4 Standard deviation of…

Q: Given a random variable Y ~ Pois(A) (a Poisson random variable with parameter ) > 0), (a) Find My…

A:

Q: 2. Let us consider a discrete random variable having the pmf given by, k = 1 Px(k) = {2 k = 2. 3' 0,…

A: We have been given the pmf as,   Px(k)=13,      k=123,      k=20,        k=3 The mgf is given by,…

Q: X is an exponential random variable with parameter λ = 4   Calculate P {X ≤ 3

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Q: Suppose that the hazard rate of a certain continuous positive random variable is given by 4t+4. Find…

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Q: Two random variables X and Y have the joint pdf, fx, y(x, y) = Ae12x+y), = 0, X, y 2 0 elséwhere (1)…

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Q: y > 0 fV) = for ß > 0. y 1.9) Give your answer to three decimal places.

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Q: X and Y be two discrete random variables with a joint p en by X-0 X-2 Y=1 0.03 0.02

A: to find P(X&gt;0 and Y≤3)

Q: (30) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) = { , find E(e*) O.w

A: It is given X is a random variable with pdf f(x) = 2e-2x,0&lt;x&lt;∞0,otherwise

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

A: Provided probability density function is, fx=2e-2x         for 0&lt;x&lt;∞=0…

Q: (27) Let X be a random variable with p.d.f. 3e-3x 0 <x< 00 f(x) =. , find E(x) O.W

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Q: Suppose that three random variables X1, X2, X3 form a random sample  from the uniform distribution…

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Q: 2. The distribution function of the random variable X is given by 1– (1+x)e¬* for x>0 F(x) = for x=0…

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Q: p.d.f. h(x) of the random variable x is defined by h(x) =3/(4(1-x²)),-1<x< 1,Calculate the standard…

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Q: 3. Let X1,..X be a random sample from f(r, 0) =, 0 0. Let Y1 = min,{X,}. Find consistent estimators…

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Q: 1 For a random variable X with mgf Mx(t) = (1–4)'/2 Find E[X²]

A: Given: The moment generating function of the random variable X is given as:…

Q: 3. Find a PDF of a random variable X whose CDF is given by Fx(x) = (1-e*)[0,00) (x).

A: Solution

Q: (a) The random variable X has probability distribution 3 5 7 9. 11 P(X=x) 0.18 0.19 Q 0.2 (i) Given…

A: Solution-: We have following table: x 3 5 7 9 11 P(X=x) 0.18 P 0.19 Q 0.2 We want to find,…

Q: Consider a random sample X1, X2, ..., X, from Bernoulli's distribu- tion B(1, p). Prove that X; is a…

A:

Q: A continuous random variable has a p.d.f. ſkx³(1 – x)²0 < x < 1 | f(x) = Ootherwise

A: Given,f(x)={kx3(1-x)2  ;0&lt;x&lt;10                   ;otherwise

Q: Let X be a beta distributed random variable having parameters a = 3.27 and 3 = 4.95. Find E[X²®(1 –…

A:

Q: Given the distribution function x < 0 1 0<x < 2 F (x) = 2 < x < 5 1 r25 of the random variable X.…

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Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

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Q: PMF of random variable X is defined as 0.2 X = -2 0.1 X = -1 0.1 X = 0 Px (x) = {0 X = 1 ve X = 2…

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Q: et X be a random variable which takes values in the interval ow that E(X)- a PIXI> a)

A: We are given,  X=Random variable which has the values between [-M, M] only. Hence, we have the…

Q: X and Y are random variables with the following joint PMF. X?, Y? 6 -7 9 9 0.2 0.1 0.16 -3 0.1 0.15…

A: From the given information, let X and Y are two random variables. The given joint probability mass…

Q: Given that a random variable X have a Poisson distribution with 2; Find E[cos(nX)] if E(X) = In 2

A: Given information: X = a Poisson random variable The expected value of X is: EX=ln 2=λ It is…

Q: Q. 2 For the exponential random variable X with parameter à = 2, compute the ollowing probabilities.…

A:

Q: Suppose that X is a Normal random variable with E(X) = 1 and Var (X) = 1. Define Y =2X + 1. Find P(0…

A: Consider, EY=E2X+1=2EX+1∵EaX+b=aEX+b=2*1+1=3 VarY=Var2X+1=22*VarX∵VaraX+b=a2*VarX=4*1=4 SDY=VarY=4=2

Q: Let xbe a Geometric random variable with p%3= 0.6. Find the mgf at zero MO)

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Q: The probabilities of all the values of a random variable X must: OA. average to a small and negative…

A: Random Variable: In probability theory, a random variable is a variable whose values depend on…

Q: The random sample X1, X2, ..., X60 is obtained from a random variable X with Hx = 5.7 and ox = 2.3.…

A: a. Here, the mean is 5.7, the standard deviation is 2.3, and the sample size is 60.

Q: The proportion of adults living in a small town who are college graduates is estimated to be p =…

A: a) From the given information, The fail to reject zone is 8≤x≤10. Rejected zone is X&lt;8 or…

Q: 2. A random variable X takes values between 0 and o with a cumulative distribution function F(x) = A…

A: Cumulative Distribution Function: Let X is a random variable (discreate or continuous). Then then…

Q: Let X1,..., X10 be a random sample of size 10 from a N(u, o²) population. Suppose 10 E(x; - 4)² Y ||…

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Q: X is an exponential random variable with parameter λ = 1/4 Calculate P {X ≤ 4}

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Q: 10. Suppose X and Y are a continuous bivariate random variable with 0SXS1 and0SYS2 and valid joint…

A: here given joint pdf of x and y  f(x,y) = c(1 + x/2 + y/4)   where  0 ≤ x ≤1 and   0 ≤y≤2

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: Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X.…

A: Given information:Given that the mean and variance of the variable X is 3 and 2.That is, E(X) = 3…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.