5. If X-Beta(a, ß) show that E(X) = and Var(X) : aß (a+B)=(a+B+1) a+B

Q: (a) Show that y for the given z = e" In x+ xy

A:

Q: 2- Suppose = {xt)dt . Find ES and d acconding the statistical characteristics of xt).

A: For a continuous random variable X, a probability density function is a function such that (1) f(x)…

Q: 16 – tª -dt t3 Integrate: + C

A:

Q: 7 Find the most general antiderivative for the function – 5VP. 2 -

A:

Q: how do you find z sub alpha over 2 using table a-2

A: I am solving this question by taking an example Let us take α = 0.05 We need to find

Q: 1 x+1 Integrate: r21?

A: Here we have, I=∫01x+1x2+2x2dx

Q: let X~beta(a,b). find m.g.f ofY=ln| 1-x

A:

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: 13.3.9 Evaluate -x)-Pdx a beta function. as

A: Use the property of beta function to evaluate this integral.

Q: 3. Find an orthonormal pair one of whose members is proportional to (4, -3).

A:

Q: 1,3 2,1 3,4 f(x) 2,6 3,5 3,2

A: The given tabular data is,

Q: Suppose you estimate the following regression function where Y, X1, and X2 are continuous variables…

A: The following solution is given below :

Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

A:

Q: 1 Integrate with respect to x. 4+ 25(3x +1)²

A:

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

A:

Q: Consider the econometric model y = Bo + B1x +u and the OLS estimator B, for B1. We know that: O…

A:

Q: If T, is an MVUE of y (0) and T, is any other unbiased estimator of y (0) with efficiency e < 1,…

A: Answer: For the given data,

Q: 2. Show that for simple linear regression (SLR) we have that cov(B, B,) = - xoʻ/S

A:

Q: IF X has an exponential distribution with the parameter 0 an Hy = 202, where 0 >0 then find µx, a,…

A: Given that X has exponential distribution with parameter θ. μx=2σx21θ=2*1θ2θ=2 Therefore,…

Q: 2. Suppose the PDF of X is given by fx(x) = 5e-5x(o)(x). Find its CDF.

A: Solution

Q: 36 – y8 -dy y5 Integrate:

A: SOLUTION-

Q: Let Ximexp (A). Show i Sulficieny that T-ZXi is Statistics

A:

Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

A:

Q: 2- Max z =30 x, + 30 x2 X +2 x2 2 80, 3x +2x2 2 120, Simppler s.t. X, X, 20

A:

Q: use the beta function to compute P(3<Y≤5).

A:

Q: In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different…

A:

Q: What are the critical points of Cobb-Douglas production function  q=K^0.2L^0.6 subject to…

A: First nwe have to change the required equation from 2 variables to a single variable.

Q: 1. Evaluate 5 S Sx (x + 3x)dydx

A: Given, ∫05∫0x x(x + 3x) dy dx=  ∫05∫0x (x2 + 3x2) dy dx=  ∫05 ∫0x (x2 + 3x2) dydx= ∫05 ∫0x 4x2 dydx

Q: In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different…

A: The events A and B are defined as follows: A : A batch is formed from two different lots B : A lot…

Q: (4) Evaluate : + yz') dV if Q= {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 2]}

A:

Q: Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order…

A: Given information: Given that the random sample X1, X2, … , Xn is from a population with probability…

Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: 2. Given f(x) = x' + ax² + bx has critical numbers at x=1 and x=3, find a and b. .2

A:

Q: An M.V.U. is unique in the sense that if T, 1 M.V.U. estimators for y (0), then T, = T, almost

A: A sample statistics t is said to be unbiased estimator of population parameterγ(θ) if expected value…

Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

A:

Q: Find the integration inner product on C[-4, 3] of the given functions. f(x) = 16x g(x) = 2x?

A:

Q: Define Beta function and hence, find x° V1– x²dx.

A:

Q: 12. Suppose an enzyme is known to obey Michaelis-Menten kinetics, but the parameters V and K are not…

A: Given:-             Suppose an enzyme is known to obey Michaeli's-Menten kinetics, but the…

Q: 8. Theorem h° = %3D

A: The figure given below represents the circle. From the angle subtended by the same arc theorem, The…

Q: Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1

A: Solution

Q: Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

A: We will find out the required result using Gramma function.

Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: 1. If X,, X2, .X, forms a random sample of size n from a population with pdf f(x; 8,8) = 0 for x>0…

A:

Q: In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different…

A: Given data in the manufacturing of a chemical adhesive 3% of all batches have raw materials from two…

Q: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

A:

Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…

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!