Homework Answers
The answer is No. Option B is correct.
This is because we have sample size which is less than 30. Therefore, according to Central Limit Theorem as sample size increases i.e. sample size is larger than 30, then first two moment around the mean of that distribution that is mean and variance will tend to normal distribution.
In this case we have n less than 30 i.e. 25 t distribution will be used in such case
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Suppose that Y....Y, are i.l.d. random variables with the probability distribution given in the figure below....
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and...
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
Suppose X, Y and Z are three different random variables. Let X obey Bernoulli Distribution. The...
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3. (20 marks) Suppose Y...Y is a random sample of independent and identically distributed Gamma(c...
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Suppose hat the joint probability distribution of the continuous random variables X and Y is cons...
Suppose hat the joint probability distribution of the continuous random variables X and Y is constant on the rectangle 0 < x < a and 0 < y < b for a, b E R+. Show mathematically that X and Y are independent. Hint: (a) Recall JDx "lly f(r, y) dy dx-1 (b) Recall X, Y are independent if ffy fry
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, Upper X 2, Upper X 3, and Upper X 4 are normally distributed random variables:...
, Upper X 2, Upper X 3, and Upper X 4 are normally
distributed random variables: Upper X 1 tilde Upper N left
parenthesis 0 comma 0 right parenthesis, Upper X 2 tilde Upper N
left parenthesis 0 comma 1 right parenthesis, Upper X 3 tilde
Upper N left parenthesis 1 comma 0 right parenthesis, and Upper X
4 tilde Upper N left parenthesis 1 comma 1 right parenthesis.
X1, X2, X3, and X4 are normally distributed random variables: X1...
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3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
Consider the following joint probability distribution on the random variables X and Y given in matrix form by Pxy P11 P12 P13 PXY-IP21 p22 p23 P31 P32 P33 P41 P42 P43 HereP(i, j) P(X = z n Y-J)-Pu represents the probability that X-1 and Y = j So for example, in the previous problem, X and Y represented the random variables for the color ([Black, Red]) and utensil type (Pencil,Pe pblackpen P(X = Black Y = Pen) = P(Black n...
3. (20 marks) Suppose Y...Y is a random sample of independent and identically distributed Gamma(c, B) random variables. Suppose c is a known constant. a) (5 marks) Find an exact (I-a)100% CI. forty: cß based on Y. Hint: Make use of the Chi-Square distribution when finding your pivot. b) (5 marks) Find an approximate (1-α)100% CI. forMy-cß based on only Y using a n (Y-CB) ~ Normal (0, Normal approximation and the pivot Z- c) (5 marks) Find an approximate...
Suppose hat the joint probability distribution of the continuous random variables X and Y is constant on the rectangle 0 < x < a and 0 < y < b for a, b E R+. Show mathematically that X and Y are independent. Hint: (a) Recall JDx "lly f(r, y) dy dx-1 (b) Recall X, Y are independent if ffy fry
Suppose hat the joint probability distribution of the continuous random variables X and Y is constant on the rectangle...
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, Upper X 2, Upper X 3, and Upper X 4 are normally
distributed random variables: Upper X 1 tilde Upper N left
parenthesis 0 comma 0 right parenthesis, Upper X 2 tilde Upper N
left parenthesis 0 comma 1 right parenthesis, Upper X 3 tilde
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