6. Show that 1 s2 = TE2-1(Xi – x)² is unbiased estimator of the population variance o?

Q: Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2.…

A: T- test is used under the assumptions Variances are equal and not equal

Q: 6.20. (a) For a group of 10 items, 10 10 E (X;-2) = 40 and i = 1 E X? = 495. i = 1 Then find the…

A:

Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

Q: 5. The variance of a random variable X is defined as the expected value of the squared deviation…

A: Given,μ=E(X)Var(X)=EX-E(X)2

Q: 3 For an SRS {Y: ³;=, from the normal distribution 1 fiy (цілето 2) vivore (y;u, - Show that the…

A: Here, The simple random samples of size n taken from the normal population. We have to show that the…

Q: 5. Let X have the pdf {(x + 1) -1 <x < 1 f(x) = elsewhere. Find the mean and the variance of X.

A: 5. The given pdf is, fx=12x+1       -1&lt;x&lt;10                   elsewhere

Q: Fix the standard deviation of variance at igma(o)=1.Sketch the graphs for N(-2,1) N(0.1) ,N(2,1).…

A: Given information: The parameters of a normal distribution are given for 3 different scenarios.

Q: Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2.…

A: Given that the random variable  represent the ith normal population with unknown mean  and unknown…

Q: 1-X = 1/(X₁ + + Xn) is an unbiased estimator for the population mean. FALSE 02 1 LIV F12 TRUE (X…

A:

Q: The PDF of the random variable X is fx (x)=-; 0<x<9. 6√x What are i) mean, ii) the mean square value…

A:

Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

A: Let X be a random variable with a cumulative distribution function (cdf) given byTo findThe…

Q: Q1. (3 points) Suppose that samples of size 36 are selected at random from a normal population with…

A:

Q: Show that (X1+ X„)/2 is an unbiased estimator of u, if {X1, ... , X„} is a random sample from the…

A: Solution

Q: Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and variance of x.

A:

Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

A:

Q: Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is…

A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

Q: Suppose P(X E {1,2,3})=1 and E(X) =2.5. What is the smallest and largest possible values for the…

A: P(x=i) =pi where i = 1,2,3 Since P(X belongs to {1,2,3}),  p1+p2+p3 = 1…

Q: If X is a Poisson variate such that 4) + 90 P(X=6), find the P(X=2)=9P variance (X =

A:

Q: Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator of

A:

Q: Suppose X = number of direct injuries occurring in a fire incident. Its PMF is given by x 0 1 2 3 4…

A: Given that  x 0 1 2 3 4 5 6 7 8 f(x) 0.08 0.08 0.09 0.14 0.18 0.16 0.09 0.06 0.06

Q: Derive that the variance of the forecasted error using Exponential Smoothing (ES) method is given by…

A: Given the variance of the forecasted error using the Exponential Smoothing (ES) method as

Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

A:

Q: In the 2012 presidential election, exit polls from the critical state of Ohio provided the following…

A: As per our guidelines, we are allowed to answer first question only. Thanks   Given Data :

Q: Suppose you fit a simple Poisson model such that In A = XB where B = 1.9. What would the variance be…

A: Given data

Q: Calculate the standard deviation of h(x) = 2x+9

A: Given x 1 3 4 6 12 P(x) 0.03 0.1 0.05 0.15 m

Q: Determine the mean and the variance of X.

A: Given that  f(x) = 0.125 x    for 0&lt;x&lt;4   We know that  Mean = E(x) = ∫x.f(x) dx variance V(x)…

Q: True or False? 1/n∑(Xi − X)^2 is an asymptotically unbiased estimator for the variance of X.

A: Here we have to check the given statement is true or false. 1/n∑(Xi − X)^2 is an asymptotically…

Q: Imagine a family member looks over your shoulder as you look at the variance equation Σki=1(xi −…

A: sigma^2   = ∑ (x −  μ)2 / n

Q: Show that variance o? (x²) – ((x))²

A: Solution