7.15 Assume that X₁, X2, X3, X4 are independent and normally distributed with E[X₁] = 100 E[X₂] = 90 E[X3] = 95 E[X4] = 105 Var[X₁] = 30 Var[X₂] = 20 Var[X3] = 25 Var[X4] = 15. (a) What is the distribution of S = X₁ +X-2 + X3 + X4? Can we use the central limit theorem in this case? (b) Find E[S], Var[S], and o [S]. (e) Compute P(S≤ 390). Is the answer different from P(S < 390)?

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A:

Q: Page 263, 4.4.5.* Let Y₁ < Y₂ < Y3 < Y4 <Y5 be the order statistics of a random sample of size n = 5…

A:

Q: 6. A chemical system that results from a chemical reaction has two important components among others…

A: Given, the joint distribution of X1 and X2 is

Q: ƒ(x) = 6x - 4x 2 x² +1 on [-3,0]

A: Let's find average value of given  function on interval [ -3 , 0 ].

Q: Determine the mean waiting time W for an M/M/2 system when lambda = 2 and μ = 1.2. Compare this with…

A:

Q: X is a normally normally distributed variable with mean µ = 30 and standard deviation o = 4. Find a)…

A:

Q: show th at E(bo) = Bo and Var (bo) = 6e Ln t. find the estimation rownd the mean Point %3D

A: Given information: It is required to find the mean and variance of the intercept of regression…

Q: Let X have PMF P(X = k) = −p^k/(k log(1 − p)) for k = 1, 2, 3, ...,where p is a parameter such that…

A: Let X be a random variable. The expected value of X or the mean of X, denoted by E(X) or μX​ is…

Q: Let x = (x₁,...,xn) be a data set, and denote its sample standard deviation with sx. Let y₁ = ax; +…

A:

Q: 2. Suppose that X is normally distributed with u =-7 and o2 P(X 2x) = 0.84. 14. Find the value of x…

A:

Q: 27. If X is uniformly distributed over (0, 1) and Y is exponentially distributed 1, find the…

A: X is uniformly distributed over (0, 1) and Y is exponentially distributed with parameter .

Q: Exercise 6. The first quartile (or 25th percentile) of the distribution of X is defined as that…

A:

Q: Suppose X = 1/(1+Y), where 12 Y ~ fy(y) = y > 0, %3D 0, Identify the distribution of X by name and…

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

Q: drivers of that Age - ]]], [16 – 17,1,55], [18 - 19,2,30], [20 - 24, 3, A traffic safety…

A: The objective of the question is to understand the data provided by a traffic safety organization in…

Q: 6. (For stat 5504 only). Let Y = X² +XZ where X and Z are independent, normally distributed and E(Z)…

A: Given :E(Z)=E(X)=2 and E(Z2)=E(X2)=3a) The predictor of Y from X. if X=1.8.b) The best linear…

Q: Let x~ exp (A) Show that T=s Xi is sufficiency Statistic.

A: Generally we use factorization theorem to obtain the sufficient statistic.

Q: indard deviation of each stock and the covariance between them. BI of

A:

Q: Suppose X has a continuous uniform distribution over the interval [1.4, 6.0]. Round your answers to…

A:

Q: Let X = the time (in 10-1 weeks) from shipment of a defective product until the customer returns the…

A: Note: Hey there! Thank you for the question. As you have posted a question with more than 3…

Q: 20. A continuous random variable X has CDF given by if x <1 F(x) ={2(x – 2 + 1/x) if 1<x<2 if 2 < x…

A: As Prof. A. K. Giri defined, "Probability Density Function: A continuous function f(x) is said to be…

Q: Let X₁, X₂,..., Xn be a random sample from an exponential distribution with the pdf e-/, for 0 < x…

A: Given that The probability density function of X f(x,β)=1/βe-x/β. 0&lt;x&lt;We have to find the…

Q: For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is…

A: It was stated that the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X…

Q: The lifetime of a machine part has a continuous distribution: Osxs 40 fx(x) = { (10+x)² else a.…

A:

Q: Suppose X~ N(2,6). What value of a has a z-score of three? x =

A: From the information, the random variable X follows normal with mean 2 and standard deviation 6.…

Q: The pandemic has caused serious problems for the Pakistan Stock Exchange (PSX). The market has been…

A: Given: Population standard deviation σ = 2000 Sample size n = 15 Sample mean X = 46000 Confidence…

Q: Find the mean and standard deviation for each uniform continuous model U(1, 13) U(70, 200) U(3, 92)

A: Obtain the mean and standard deviation for the uniform continuous model U(1,13). Obtain the mean of…

Q: nstants аnd 9. Fx (x) = [1 – a. e-x/b]u (x) is a valid distribution funetion. u (x) is an unit step…

A: Answer: For the given data

Q: Assume δ = 0.05, ̄Ax = 0.06, 2 ̄Ax = 0.0040. A group of 100 lives age x purchase fully continuous…

A: Given  δ=0.05 A¯x=0.06 A¯x2=0.0040 Benefit=$1000 Premium=$3.50

Q: 5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the pdf of…

A: X is continuous uniform distribution in the interval (a,b). X ~ U(a,b) So, Variance of X, Var(X) =…

Q: 3. Let X be a continuous random variable on the interval [0, 1] having cdf Fx(x) = 3x² − 2x³. Let W…

A:

Q: Let X1, X2, ..., Xn be a random sample having the common pdf f(xr, 0) = exp[-(x – 0)] for r2 0. (i)…

A:

Q: Find the values of constants 'a' and b' such that Fx (x) = [1-a ·e*/b] u (x) is a valid distribution…

A:

Q: 7) Allow a continuous probability distribution to be defined as f(x) = x/2 for the range 0 sxs2. %3D…

A:

Q: In this question you are required to examine distribution at X(0) and x(1/8fo) x(0) ∈{0,-1 ,1}…

A: Given information: The distributions of X(0) and X(1/8fo) are given.

Q: Let X denote the mean of a random sample of size 25 from the distribution whose pdf is f(x) = x²…

A: We have given that the X-bar denote the mean of a random sample of size 25 from the distribution…

Q: et X1,..., Xn be a random sample from a uniform distribution on the interval [20,0], where 0. et…

A: Solution

Q: If a continuous RVX (> 0) possesses memoryless property, that is P(X>x+h)= P(X > x). P(X > h), then…

A:

Q: Suppose the distribution of waiting times (in hours) for residents of a particular province trying…

A: From the given information, f(t)=56e-5t6, t&gt;0 Mean waiting time: E(t)=∫0∞tf(t)dt…

Q: Estimate In(5) using linear interpolation if In(1)=O and In(6)=1.7917.

A:

Q: 6. Show that a gamma distribution with a > 1 has a relative maximum at x = (a- 1)ß. What happens…

A: Relative maximum =? For a gamma distribution for alpha&gt;1

Q: Suppose X~ Uniform [10, 50], find: 1. P70 2. Variance (X)

A: