Assume X ~ ? (10, 4) where ? implies unknown. 1. What is the (approximate) distribution...

Assume X ~ ? (10, 4) where ? implies unknown.

1. What is the (approximate) distribution of x if the sample size is 100? Briefly discuss the theorem underlying your answer.

2. What happens to the variance of x as the sample size increases? Draw a diagram and explain.

3. What two values of x (symmetric around the population mean) contain a) 75% and b) 95% of the distribution? Draw a diagram. Relate your answer to b) to the empirical rule.

Expert Solution

Solution:

** Please rate the answer if you liked it by clicking on thumbs-Up. Thank-you

orchestra answered 2 years ago

Assume X ~ ? (10, 4) where ? implies unknown. What is the (approximate) distribution of...

Assume X ~ ? (10, 4) where ? implies unknown. What is the (approximate) distribution of if the sample size is 100? Briefly discuss the theorem underlying your answer. What happens to the variance of as the sample size increases? Draw a diagram and explain. What two values of (symmetric around the population mean) contain a) 75% and b) 95% of the distribution? Draw a diagram. Relate your answer to b) to the empirical rule.

Assume X ~ ? (10, 4) where ? implies unknown. What two values of (symmetric around...

Assume X ~ ? (10, 4) where ? implies unknown. What two values of (symmetric around the population mean) contain: a) 75% and b) 95% of the distribution? Draw a diagram. Relate your answer to b) to the empirical rule.

. Assume X ~ N (10, 4). What is the (approximate) distribution of X if the...

. Assume X ~ N (10, 4). What is the (approximate) distribution of X if the sample size is 100? Briefly discuss the theorem underlying your answer. What happens to the variance of as the sample size increases? Draw a diagram and explain. What two values of (symmetric around the population mean) contain a) 75% and b) 95% of the distribution? Draw a diagram. Relate your answer to b) to the empirical rule.

Assume that X has a Poisson distribution with mean of 3.7. Calculate the followings. P(X=1) P(1<X<4)...

Assume that X has a Poisson distribution with mean of 3.7. Calculate the followings. P(X=1) P(1<X<4) P(1<X<2) P(2<X<4) P(X=1.5) P(X=0) P(X<-2) Standard Deviation of X Mean of X

A random variable X has a distribution p(X=k) = A / (k(k+1)), k = 1,2,...,4, where...

A random variable X has a distribution p(X=k) = A / (k(k+1)), k = 1,2,...,4, where A is an constant. Then compute the value of p(1<=X<=3) The answer will be either: 2/3, 3/4, 5/6, or 15/16 A discrete random variable X is uniformly distributed among −1,0,...,12. Then, what is its PMF for k=−1,0,...,12 The answer will be either: p(X = k) = 1/12, 1/13, 1/14, or 1

1)(a) Approximate the value of the double integral, ∫ ∫ R x 2 ydA, where R...

1)(a) Approximate the value of the double integral, ∫ ∫ R x 2 ydA, where R = [−1, 5] × [0, 4], using the midpoint rule with m = 3 and n = 2. (b) Evaluate the double integral in the part (a), evaluating the corresponding iterated integral. 2)Let D be a region in the xy plane, between the graphs of y = 2 cos(x) and y = − sin(x), for 0 ≤ x ≤ π 2 . Sketch D...

The mean of the binomial distribution 10∁x ( 2/3 )^x ( 1/3 ) ^ 10 -x...

The mean of the binomial distribution 10∁x ( 2/3 )^x ( 1/3 ) ^ 10 -x is given by

Use Newton’s Method to approximate the value of x where f(x) = x3 + 10x2 +...

Use Newton’s Method to approximate the value of x where f(x) = x3 + 10x2 + 15x – 2 has a local maximum. Give the value accurate to 3 decimal places.

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x)...

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is concave up, and the intervals where f(x) is concave down, and the inflection points of f(x) by the following steps: i. Compute f 0 (x) and f 00(x). ii. Show that f 00(x) is equal to 0 only at x = −2 and x = 2. iii. Observe that f 00(x) is a continuous since it is a polynomial. Conclude that f 00(x)...

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1,...

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1, 2, ..., and 0 < p < 1. This form of the geometric starts at x = 0, not at x = 1. Given are the following properties: E(X) = (1-p)/p, and Var(X) = (1-p)/p^2 A random sample of size n is drawn; the data are X1, X2, ..., Xn. A. Derive the Fisher information function for the parameter p. B. Find the Cramér-Rao...

Question