![1l. Suppose that X1, X2,... Xn are independent random variables. Assume that ElXi] /4 and Var(X )-σ, where i 1, 2, . .., n. If ai , aam. , an are constants. 1,a2, , an are constan (i) Write down expression for (i) E{Σ,i ai Xi) and (ii) Var(Li la(Xi). (i) Rewrite the expression if X,s are not independent.](http://img.homeworklib.com/questions/ab2fd0e0-77e5-11ea-9eaf-c94a23a0f162.png?x-oss-process=image/resize,w_560)
Homework Answers
(i)
X1 , X2 , .... , Xn are
independent random variables 
Cov(Xi , Xj) = 0 
i,j=1,2,...,n ; i
j
(ii)
X1 , X2 , .... , Xn are not independent random variables.
Let 
ij be the correlation between Xi and
Xj
i,j=1,2,...,n ; ij
Cov(Xi , Xj) =
ij
ij
i,j=1,2,...,n ; ij
Add Answer to:
explan the answer
1l. Suppose that X1, X2,... Xn are independent random variables. Assume that ElXi]...
explan the answer . Suppose that Xi, X2,.... Xn are independent random variables. Assume that E[A]-:...
explan the answer . Suppose that Xi, X2,.... Xn are independent random variables. Assume that E[A]-: μί ald Var(Xi)-σ? where i-| , 2, , n. If ai, aam., an are constants. (i) Write down expression for (i) E{E:-aiX.) and (ii) Var(Σ-lai%). (i) Rewrite the expression if X,'s are not independent.
3. Suppose that X1, X2, , Xn are independent random variables with the same expectation μ...
3. Suppose that X1, X2, , Xn are independent random variables with the same expectation μ and the same variance σ2. Let X--ΣΑι Xi. Find the expectation and variance of
. If X1, X2,..., Xn are independent random variables with common mean μ and variances σ1,...
. If X1, X2,..., Xn are independent random variables with common mean μ and variances σ1, σ2, . . ., σα , prove that Σί (Xi-T)2/[n(n-1)] is an ว. 102n unbiased estimate of var[X] 3. Suppose that in Exercise 2 the variances are known. LeTw Σί uiXi
L.11) Sums of independent random variables a) If X1 , X2 X, , , Xn are...
L.11) Sums of independent random variables a) If X1 , X2 X, , , Xn are independent random variables all with Exponential μ distribution, then what is the distribution of XII + 2 +X3 + .tX b) If X is a random variable with Exponential[u] distribution, then what is the distribution of x +X1? c) If X1 , X2 , Х, , , X are independent random variables all with Normal 0. I distribution, then what is the distribution of...
How do you show this? 1.2.12. Accept the following definition. Discrete random variables X1, X2,.. ,...
How do you show this?
1.2.12. Accept the following definition. Discrete random variables X1, X2,.. , Xn, taking values in Ai, A2,..., An, are said to be independent if (1) P(Xi = ai , . . . ,x, = an) =11P(X, = a.) 仁1 for all ai E A1,., an E An. Then prove that random variables in any subsequence of a finite sequence of independent random variables are independent.
1. Let X1, ... , Xn be independent random variables taking values 0 or 1 with...
1. Let X1, ·s, Xn be independent random variables taking values 0 or 1 withP(Xi=1)=eθ-ai /(1+eθ-ai ), i=1, ……, nfor some given constants ai. Find a one-dimensional sufficient statistic for θ.
Suppose X1, X2,... are independent Geometric (number of trials) random variables where Xi ~ Geome...
Suppose X1, X2,... are independent Geometric (number of trials)
random variables where Xi ~ Geometric(p = 1/i^2)
a) It is easily shown that Xn converges to a for some constant
a. Name it.
b) According to the Borel-Cantelli Lemmas, does Xn almost surely
converge to a?
Suppose Xi, X2, are independent Geometric (number of trials) random variables where x,~ Geometric(pal+) |. a) It is easily shown that Xa for some constant a. Name it. b) According to the Borel-Cantelli Lemmas,...
Let X1, X2, ....,. Xn, be a set of independent random variables, each distributed as a...
Let X1, X2, ....,. Xn, be a set of independent random variables, each distributed as a normal random variable with parameters μί and σ. Let х, ai Use properties of moment generating functions to determine the distribution of Y, meaning: find the type of distribution we get, and its expected value and variance
Let X1, X2, , xn are independent random variables where E(X)-? and Var(X) ?2 for all...
Let X1, X2, , xn are independent random variables where E(X)-? and Var(X) ?2 for all i = 1, 2, , n. Let X-24-xitx2+--+Xy variables. is the average of those random Find E(X) and Var(X).
Suppose the random variables X1, X2, ..., Xn are independent each with the distribution 020 *;...
Suppose the random variables X1, X2, ..., Xn are independent each with the distribution 020 *; 0) (0+1); X2 2. Find the Maximum Likelihood estimate for 0. On Žin(x) + • 8Žin(x) + n In(2) i= 1 { ince) -- OD. Žince) - n ince) -n In(2) i= 1 O e. None of the above.
explan the answer . Suppose that Xi, X2,.... Xn are independent random variables. Assume that E[A]-: μί ald Var(Xi)-σ? where i-| , 2, , n. If ai, aam., an are constants. (i) Write down expression for (i) E{E:-aiX.) and (ii) Var(Σ-lai%). (i) Rewrite the expression if X,'s are not independent.
3. Suppose that X1, X2, , Xn are independent random variables with the same expectation μ and the same variance σ2. Let X--ΣΑι Xi. Find the expectation and variance of
. If X1, X2,..., Xn are independent random variables with common mean μ and variances σ1, σ2, . . ., σα , prove that Σί (Xi-T)2/[n(n-1)] is an ว. 102n unbiased estimate of var[X] 3. Suppose that in Exercise 2 the variances are known. LeTw Σί uiXi
L.11) Sums of independent random variables a) If X1 , X2 X, , , Xn are independent random variables all with Exponential μ distribution, then what is the distribution of XII + 2 +X3 + .tX b) If X is a random variable with Exponential[u] distribution, then what is the distribution of x +X1? c) If X1 , X2 , Х, , , X are independent random variables all with Normal 0. I distribution, then what is the distribution of...
How do you show this?
1.2.12. Accept the following definition. Discrete random variables X1, X2,.. , Xn, taking values in Ai, A2,..., An, are said to be independent if (1) P(Xi = ai , . . . ,x, = an) =11P(X, = a.) 仁1 for all ai E A1,., an E An. Then prove that random variables in any subsequence of a finite sequence of independent random variables are independent.
1. Let X1, ·s, Xn be independent random variables taking values 0 or 1 withP(Xi=1)=eθ-ai /(1+eθ-ai ), i=1, ……, nfor some given constants ai. Find a one-dimensional sufficient statistic for θ.
Suppose X1, X2,... are independent Geometric (number of trials)
random variables where Xi ~ Geometric(p = 1/i^2)
a) It is easily shown that Xn converges to a for some constant
a. Name it.
b) According to the Borel-Cantelli Lemmas, does Xn almost surely
converge to a?
Suppose Xi, X2, are independent Geometric (number of trials) random variables where x,~ Geometric(pal+) |. a) It is easily shown that Xa for some constant a. Name it. b) According to the Borel-Cantelli Lemmas,...
Let X1, X2, ....,. Xn, be a set of independent random variables, each distributed as a normal random variable with parameters μί and σ. Let х, ai Use properties of moment generating functions to determine the distribution of Y, meaning: find the type of distribution we get, and its expected value and variance
Let X1, X2, , xn are independent random variables where E(X)-? and Var(X) ?2 for all i = 1, 2, , n. Let X-24-xitx2+--+Xy variables. is the average of those random Find E(X) and Var(X).
Suppose the random variables X1, X2, ..., Xn are independent each with the distribution 020 *; 0) (0+1); X2 2. Find the Maximum Likelihood estimate for 0. On Žin(x) + • 8Žin(x) + n In(2) i= 1 { ince) -- OD. Žince) - n ince) -n In(2) i= 1 O e. None of the above.
Most questions answered within 3 hours.
-
Water at gauge pressure of 3.8 atmospheres at street level
enters an office building at 0.60...
asked 11 minutes ago -
Quick question, I want to know how to convert decimal numbers to
binary number, when i...
asked 32 minutes ago -
You found out that now you are going to receive payments of
$8,500 for the next...
asked 36 minutes ago -
17.
Technician A says that leaking components are usually repaired
rather than replaced. Technician B says...
asked 37 minutes ago -
A) An Operon is:?
1- A gene that affect another gene
transcription.
2. A gene coding...
asked 43 minutes ago -
When opening a file, use this method to determine whether a file
exists before you attempt...
asked 48 minutes ago -
Sales total $300,000 when variable costs total $180,000 and
fixed costs are $60,000. Breakeven sales total:...
asked 54 minutes ago -
1)
To calculate the depth of a water well, an explorer drops a stone and with...
asked 52 minutes ago -
0.429-g sample of gas occupies 125 mL at 60. cm of Hg and 25°C.
The molar...
asked 54 minutes ago -
The
pH of a 0.90M solution of boric acid (H3BO3) is measured to be
4.64.
Calculate...
asked 1 hour ago -
on april 10, a company acquired land valued at $58,000 in
exchange for 1,000 shares of...
asked 1 hour ago -
Is
ampicillin or solvents (such as acetone) more effective at killing
off bacteria, in general? Explain...
asked 1 hour ago