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Chapter 15: Q17P (page 743)

Find the number of ways of putting2particles in4boxes according to the three kinds of statistics.

Short Answer

Expert verified

The required values are mentioned below.

M=16M=6M=10

Step by step solution

01

Given Information.

The two particles are in four boxes.

02

Definition of uniform sample spaces.

If a given experiment's sample space is known to be uniform, the probability of an event can be calculated using the event sizes and the sample space.

03

Find the methods

The formula for Maxwell-Boltzmann states that M=nN.

M=42=16

Use Fermi-Dirac method.

M=C(N,n)=C(4,2)=6

Use Bose Einstein method.

M=C(n鈭�1+N,n)=C(5,2)=10

Hence, the required valuesare given below.

M=16M=6M=10

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Most popular questions from this chapter

Assuming a normal distribution, find the limits渭卤hfor a 90%confidence interval; for a 95%confidence interval; for a 99%confidence interval. What percent confidence interval is渭卤1.3蟽?Hints: See Section8, Example3, and Problems,8.7,8.22 and8.23.

Two cards are drawn from a shuffled deck. What is the probability that both are aces? If you know that at least one is an ace, what is the probability that both are aces? If you know that one is the ace of spades, what is the probability that both are aces?

Answer

Let x1,x2,..,xnbe independent random variables, each with density function f(x), expected value渭 , and variance蟽2 . Define the sample meanby.x鈭�=鈭�i=1nxiShowthatE(x鈭�)=渭,and .var(x鈭�)=蟽2n (See Problems 5.9,5.13and6.15.)

Suppose that Martian dice are 4-sided (tetrahedra) with points labeled 1鈭�4. When a pair of these dice is tossed, let x be the product of the two numbers at the tops of the dice if the product is odd; otherwisex=0.

(a) A weighted coin hasprobability23 ofcoming up heads and probability13of coming up tails. The coin is tossed twice. Let x = number of heads. Set up the sample space for x and the associated probabilities.

(b) Find x and 蟽.

(c)If in (a) you know that there was at least one tail, what is the probability that both were tails?
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