Question

In: Statistics and Probability

Suppose you take samples from variable X (which is uniformly distributed). How will the distribution of...

Suppose you take samples from variable X (which is uniformly distributed). How will the distribution of sample means look? Explain

Solutions

Expert Solution

Answer:

We know that the distribution of sample gets closer to normal distribution as sample size increases irrespetive of underlying population.

As given question talks about samples from variable X which is uniformly distributed lets say large samples, the sample means will be approximately normally distributed due to CLT.

Also, it is known that the sample mean of a sample of size 2 from uniform distribution gives a triangular distribution. Sampling from larger sizes only makes the appearence of distribution more bell shaped.

***please ask if you have any doubts.Happy to help you.Thank you.Please Like.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Suppose we have a random variable X that is uniformly distributed between a = 0 and...
Suppose we have a random variable X that is uniformly distributed between a = 0 and b = 100. What is σ X? a. 0.913 b. 0.833 c. 50 d. 7.071
X ~ N (60, 9). Suppose that you form random samples of 25 from this distribution....
X ~ N (60, 9). Suppose that you form random samples of 25 from this distribution. Let  X−be the random variable of averages. Let ΣX be the random variable of sums. To make you easy, drawing the graph, shade the region, label and scale the horizontal axis for  X− and find the probability. X−~ N (60, 9/ 25) 9) P (X−< 60) = _____ a. 0.4 b. 0.5 c. 0.6 d. 0.7 10) Find the 30th percentile for the mean. a. 0.56...
A random variable x is uniformly distributed between 20 and 52 . What is the expected...
A random variable x is uniformly distributed between 20 and 52 . What is the expected value of x?
Random variable X is uniformly distributed over the interval [2, b]. Given: P { |X –...
Random variable X is uniformly distributed over the interval [2, b]. Given: P { |X – 4 | > 4} = 0. 8. a) Find P { 0 < X < 5}
X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. A. Find the 30th percentile. (Round your answer to two decimal places.) B. Sketch the graph, shade the region, label and scale the horizontal axis for X,and find the probability. (Round your answer to four decimal places.) P(66 < X < 72) = C. Sketch the graph, shade the...
X ~ N(50, 11). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(50, 11). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. A. Find the 40th percentile. (Round your answer to two decimal places.) B. Sketch the graph, shade the region, label and scale the horizontal axis for X and find the probability. (Round your answer to four decimal places.) P(48 < X < 54) = C. Sketch the graph, shade...
X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. 1. Find the 30th percentile. (Round your answer to two decimal places.) 2. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(66 < X < 72) = 3. Sketch the graph, shade...
X ~ N(50, 13). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(50, 13). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. Part (a) Sketch the distributions of X and X on the same graph. A B) C)D) Part (b) Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.) X ~ ____(____,____) Part (c) Sketch the graph, shade the region, label and scale the horizontal...
X ~ N(60, 12). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(60, 12). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. Find the 20th percentile. (Round your answer to two decimal places.)
X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let X bar be the random variable of averages. Let ΣX be the random variable of sums. Find the 40th percentile
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT