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Chapter 15: Q5P (page 749)

A random variable x takes the values with probabilities 512,13,112,16.

Short Answer

Expert verified

The required values are mentioned below.

μ=1var(x)=76σ=76

Step by step solution

01

Given Information

A random variable x.

02

Definition of the cumulative distribution function

The likelihood that a comparable continuous random variable has a value less than or equal to the function's argument is the value of the function.

03

Find the values

The mean is given below.

μ=∑0×5pxiμ=0×512+1×13+2×112+3×16μ=1

The variance is given below.

var(x)=∑xi−μ2pxivar(x)=0-12×512+1-12×13+×112+3-12×16var(x)=76

The standard deviation is given below.

σ=var(x)σ=76

Thegraph is shown below.

Hence, the required values are mentioned below.

μ=1var(x)=76σ=76

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Most popular questions from this chapter

Given the measurements.

x:98,101,102,100,99y:21.2,20.8,18.1,20.3,19.6,20.4,19.5,20.1Find the mean value and the probable error of x−y,  x/y,  x2y3and .yln(x)

Set up an appropriate sample space for each of Problems 1.1 to 1.10 and use itto solve the problem. Use either a uniform or non-uniform sample space or try both.

Three coins are tossed; what is the probability that two are heads and one tails? That the first two are heads and the third tails? If at least two are heads, what is the probability that all are heads?

Set up several non-uniform sample spaces for the problem of three tosses of a coin

:(a) Suppose that Martian dice are regular tetrahedra with vertices labelled 1 to 4. Two such dice are tossed and the sum of the numbers showing is even. Let x be this sum. Set up the sample space for x and the associated probabilities.

(b) Find E(x) and.

(c) Find the probability of exactly fifteen 2’s in 48 tosses of a Martian die using the binomial distribution.

(d) Approximate (c) using the normal distribution.

(e) Approximate (c) using the Poisson distribution.

(a) There are 3 red and 5 black balls in one box and 6 red and 4 white balls in another. If you pick a box at random, and then pick a ball from it at random, what is the probability that it is red? Black? White? That it is either red or white?

(b) Suppose the first ball selected is red and is not replaced before a second ball

is drawn. What is the probability that the second ball is red also?

(c) If both balls are red, what is the probability that they both came from the same box?
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