4.77 A random variable X has a mean u = 10 and a variance o = 4. Using Chebyshev's theorem, find (a) P(|X – 10| 2 3); (b) P(|X – 10| < 3); (c) P(5 < X < 15); (d) the value of the constant c such that P(|X – 10| > c) < 0.04.

4.77 A random variable X has a mean u = 10 and a variance o = 4. Using Chebyshev's theorem, find (a) P(|X – 10| 2 3); (b) P(|X – 10| < 3); (c) P(5 < X < 15); (d) the value of the constant c such that P(|X – 10| > c) < 0.04.

Name: 4.77 A random variable X has a mean u = 10 and avariance o = 4. Using
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: 4.77 A random variable X has a mean u = 10 and avariance o = 4. Using Chebyshev's theorem, find(a) P(|X – 10| 2 3);(b) P(|X – 10| c) < 0.04.

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

Related questions

Q: (10) For the above problem verify that the theorem of total variance (TTV) holds. The following…

A: Given that X, Y have a bivariate normal density with respective means μx, μy respective variances…

Q: 1.4 Let X be a continuous random variable with pdf, fx(x), and fx (t+5) = fx (5 t) for all t> 0.…

A: Here, we have given a continuous random variables and also some condition is given. Then, we have to…

Q: If X is normally distributed with a mean of 6 and a variance of 25, P(|X-6|<5) P(|X-6|<10)…

A: As per guideline expert have to answer first three subparts only dear student please upload other…

Q: (a) Find the expectation E (X) of X. E (X) = [] (b) Find the variance Var(X) of X. Varlx) = D

A: The following table shows the provided outputs of the discrete random variables, along with the…

Q: The values of x and their probabilities are listed below. Calculate the intermediate products to…

A: x P(x) xP(x) 32 0.07 2.24 34 0.12 4.08 36 0.24 8.64 38 0.25 9.5 40 0.32 12.8 Total…

Q: Consider a random variable X with the following pdf: fx (x) 2/9 1/9- 0 + 3 6 8 a) What is P(X ≤ 5)?…

A: PDf of random variable X is:

Q: The values of x and their probabilities are listed below. Calculate the intermediate products to…

A: Given that: x P(x) x * p(x) 32 0.07 2.24 34 0.12 4.08 36 0.24 8.64 38 0.25 9.50 40 0.35…

Q: The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors…

A: x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 X 6 0.220 7 0.136 8 0.055 9…

Q: E(X2) is greater or equal to [ E(X)2] . Hint: Recall the definition of variance.

A: E(X) implies mean of X and E(X2) implies mean of X2. Variance measures how far a set of number is…

Q: x < -1 Fx(x) = x/4+1/2 -1 < x < 1 %3D 1 Sketch the CDF and then find the following: a) P[X < 1] and…

Q: The PMF for X- the number of major defects on a randomily selected gas stove of a certain type is…

Q: When a man observed a sobriety checkpoint conducted by a police department, he saw 660 drivers were…

A: Probability theorem : P(W)+P(W¯ ) = 1

Q: Let X1,...,Xn be a random sample from a distribution with mean μ and variance σ2. Find the value of…

A: Assume that the random samples X1,..., Xn come from a distribution with mean μ and variance σ.2Then…

Q: f (x) = c/x3 for 1 < x < ∞; Find the constant c so that f (x) is a pdf of some random variable X,…

A: Given the functionwant to find the value of c such that the given function will be pdf. also wants…

Q: (b) Determine the p.m.f. or p.d.f. of Y, whichever is appropriate. (c) Compute P{Y = 1/2}.

A: Note: According to Bartleby guidelines expert solve only one question and maximum three subpart of…

Q: A researcher claims that the number of homicide crimes by season is uniformly distributed. To test…

Q: Suppose that X is a random variable for which the m.g.f. is as follows: M(t) = 1/4(3et+e-t), -∞<t<∞…

A: We can get the mean and variance after finding the first and second derivative of mgf at t= 0

Q: f (x) = c/x3 for 1 < x < ∞; Find the constant c so that f (x) is a pdf of some random variable X,…

A: Let X be a continuous random variable and it is given thatf(x)=cx3 ;1<x<∞To find:Constant…

Q: Find SD(6X+ 9).

A: solution given that, The Standard deviation of x ,denoted by SD(x)SD(x)=sqr(var(x))SD(x)=9 so , find…

Topic Video

Question

4.77 A random variable X has a mean u = 10 and a
variance o = 4. Using Chebyshev's theorem, find
(a) P(|X – 10| 2 3);
(b) P(|X – 10| < 3);
(c) P(5 < X < 15);
(d) the value of the constant c such that
P(|X – 10| > c) < 0.04.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

hoosing among several different estimators of 0, select one that is unbiased. Example 9.3: Let X₁, X2, ..., Xn be a random sample from a population mean and variance o². Show that the sample variance, - Σ(x₁ - x)² = n-1 is an unbiased estimator of o². 5²
Find the standard deviation. Р(x) | x*Р(x) (x - 4)°P(x) 2 0.1 2(0.1) = 0.2 4 0.3 4(0.3) = 1.2 6 0.4 6(0.4) = 2.4 8 0.2 8(0.2) = 1.6 00
f (x) = c/x3/4 for 0 < x < 1; Find the constant c so that f (x) is apdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphsof the pdf f (x) and the cdf F (x), and find the mean μ and variance σ2.
f (x) = 4xc for 0 ≤ x ≤ 1 ; Find the constant c so that f (x) is apdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphsof the pdf f (x) and the cdf F (x), and find the mean μ and variance σ2.
Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0
Q. 4 Let X be a chi-square random variable with degree of freedom 6 (a) Find the quantile Q(0.95) and Q(0.050); (b) Let Y be a gamma random variable with a =3 and ß =- Then find 4 P(3.28< X < 25.2).
Can you help me please:
Find the standard deviation. P(x) x*P(x) (x - )?P(x) 0.1 2(0.1) = 0.2 | (2 – 5.4)²(0.1) = 1.156 4 0.3 4(0.3) = 1.2 | (4 – 5.4)²(0.3) = 0.588 6 0.4 6(0.4) = 2.4 (6 – 5.4) (0.4) = 0.144 %3D 8 0.2 8(0.2) = 1.6 | (8 – 5.4)(0.2) = 1.352 %3D %3D Table 4.24
Suppose X and Y are independent, X has mean 5 and variance 9, Y has mean -3 and variance 6. Compute a. E[(3X + 2Y)(X + 4Y + 7)]. b. Var [6XY]
(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.
Let X be a random variable with pmf P(O)=0.2, P(1)-0.5, P(2)=0.3. Let F(X) be the cdf of X. (a) Find P(X<0.7) (b) Find F(1.3). (c) Find F(3).
Consider a random sample X1,..., X, with n > 3 from the exponential distribution with parameter ) > 0 and density 1 f(x; A) = x > 0. Consider the following two estimators of X: 3 1 ΣΧ, Ã = nX(1). 3 i=1