A sample of size n=16 isdrawn from a normallydistributed population withE(X)=20 and SD(X)=8.Find (a) P(X > 24)(b) P(16 < X < 24)0.06Population0.050.04-N(20,8)0.030.020.014 08 56 10.4 15.2 20 24.8 29.6 34.4 39.2 44 X

Answered: Image /qna-images/answer/40b134a2-bdc4-49b4-b9a0-b9beaaeb28ac.jpg

Answered: A sample of size n=16 is drawn from a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

1.9.18. Find the mean and the variance of the distribution that has the cdf x <0 0
6.2.2 If (x₁, ..., xn) is a sample from a Bernoulli(0) distribution, where 0 = [0, 1] is unknown, then determine the MLE of 0. 6.2.3 If (x₁,...,xn) is a sample from a Bernoulli(0) distribution, where 0 = [0, 1] is unknown, then determine the MLE of 0².
Let X₁,..., Xn be a random sample from a distribution with one of two pdfs. If 0 = 1, then f(x;0=1) = 1 (0 < x < 1). If 0 = 2, then f(x;0= 2) = 2x1 (0 < x < 1). (a) Give a general form of the MLE of 0. (b) You are given a sample data of 3 values: 0.4, 0.5, 0.8. Find the MLE estimate of 0 based on the data.
6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1
1. Consider a random sample of size n drawn from a population with mean ux and variance o. Show that: (a) Xn is an unbiased estimator of ux. (E{Xn}= µx or E {(Xn – µx)} = 0) - (b) X = E i where I = E, i, is an unbiased estimator of ux ixi (c) E {(X, – #x)²} = n (d) š? Σ--Χ.)2 is a biased estimator of o. n To prove or show this you will want to rewrite the expression for S2 adding and subtracting µx: E(X; - Hx + Hx - Xn)² n Rearrange this to get to the point where you are taking the expectations of known expressions: expectation from (a) expectation from (c) E{X;} = µx or E{(X; – µx)} = 0 E{(X; – Hx)²} = o%) (e) The sample variance, S? = LisXi-Xn)* is an unbiased estimator of o?. (Use the п-1 same approach as (d))
Consider a set of data x1, x2, n n i=1 ..., n taken from a population with mean µ. - Show that (x-μ)² = Σ(x₂ − x)² + n(x − µ)². i=1
With a sample size of 5, the P(t<x)=0.57P(t<x)=0.57. What is xx
(a) Let Y be a random variable distributed as X. Determine E(Y) in terms of r. (b) Let {X1, X2, . .. , Xn} be a random sample drawn from a normal distirbution with mean u and 1 variance o?. Denote S E-(X; – X)² as the sample standard deviation. Use the 1 n - result in part (a), or otherwise, to find E(S). (c) Find an unbiased estimator for the population standard deviation o.
Please state your assumptions and show all your work clearly. 1. Show that the following equalities hold: a) Population variance: N 'i=1 i=1 N N b) Sample variance: E,(xi – x)² E-,(x;)² n(x)? i=1 n – 1 n – 1 n – 1 c) Sum of differences from the population mean: Σα. > (xi – u) = 0 | i=1
4-52. If f(x) =e ,- co
Suppose that insurance companies did a survey. They randomly surveyed 450 drivers and found that 300 claimed to always buckle up. We are interested in the population proportion of drivers who claim to always buckle up. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) (i) x = (ii) n = (ii) p'= (rounded to four decimal places) O Part (b) A Part (c) Which distribution should you use for this problem? (Round your answer to four decimal places.) P'- Explain your choice. O The normal distribution should be used because we are interested in proportions and the sample size is large. O The Student's t-distribution should be used because we do not know the standard deviation. O The Student's t-distribution should be used because Vnpg s 10, which implies a small sample. O The binomial distribution should be used because there are two outcomes, buckle up…
18 Given o = (aX + 3Y) where X and Y are zero - mean random variables with variances o =4 and o= 16. Their correlation coefficient is p=- 0.5 %3| (a) Find a value for the parameter 'a' that minimizes the mean value of w (b) Find the minimum mean value.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

A sample of size n=16 is drawn from a normally distributed population with E(X)=20 and SD(X)=8. Find (a) P(X > 24) (b) P(16 < X < 24) 0.06 Population 0.05 0.04 N(20,8) 0.03 0.02 0.01 4 08 56 10.4 15.2 20 24.8 29.6 34.4 39.2 44 X