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Chapter 15: Q6P (page 749)

A card is drawn from a shuffled deck. Let x=10if it is an ace or a face card; x=鈭�1if it is a2 ; andx=0 otherwise.

Short Answer

Expert verified

The required values are mentioned below.

渭=3var(x)=28413蟽=4.67

Step by step solution

01

Given Information

A card is drawn from a shuffled deck.

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.

渭=鈭�xiPi渭=10脳1652鈭�1脳452渭=3

The variance is given below.

var(x)=鈭�xi鈭�渭2pxivar(x)=10-32脳1652+-1-32脳452+32脳3252var(x)=28413

The standard deviation is given below.

蟽=var(x)蟽=28413蟽=4.67

Thegraph is shown below.

Hence, the required values are mentioned below.

渭=3var(x)=28413蟽=4.67

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Most popular questions from this chapter

(a) Following the methods of Examples 3,4,5, show that the number of equally likely ways of putting N particles in n boxes,n>N, nNisfor Maxwell Boltzmann particles, C(n,N)for Fermi-Dirac particles, C(n鈭�1+N,N)andfor Bose-Einstein particles.

(b) Show that if n is much larger than N (think, for example, ofn=106,N=10), then both the Bose-Einstein and the Fermi-Dirac results in part (a) contain products of N numbers, each number approximately equal to n. Thus show that for n N, both the BE and the FD results are approximately equal tonNN!which is1N!times the MB result.

Two cards are drawn at random from a shuffled deck.

  1. What is the probability that at least one is a heart?

(b) If you know that at least one is a heart, what is the probability that both are

hearts?

A bit (meaning binary digit) is 0 or 1. An ordered array of eight bits (such as01101001) is a byte. How many different bytes are there? If you select a byte at random, what is the probability that you select 11000010? What is the probability thatyou select a byte containing three 1鈥檚 and five 0鈥檚?

(a) Find the probability density function f(x)for the position x of a particle which is executing simple harmonic motion on (鈭�a,a)along the x axis. (See Chapter 7 , Section 2 , for a discussion of simple harmonic motion.) Hint: The value of x at time t is x=acos蝇t. Find the velocity dxdt ; then the probability of finding the particle in a given dx is proportional to the time it spends there which is inversely proportional to its speed there. Don鈥檛 forget that the total probability of finding the particle somewhere must be 1.

(b) Sketch the probability density function f(x)found in part (a) and also the cumulative distribution function f(x) [see equation (6.4)].

(c) Find the average and the standard deviation of x in part (a).

A bank allows one person to have only one savings account insured to $100,000.However, a larger family may have accounts for each individual, and also accountingthe names of any 2 people, any 3 and so on. How many accounts are possible for afamily of 2? Of 3? Of 5? Of? Hint: See Problem 2.
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