Question

Asked Nov 10, 2019

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Choose a number B at random from the interval [0, 1] with uniform density. Find the probability that

(a) 1/3 < B < 2/3

(b) |B − 1/2| ≤ 1/4

(c) B < 1/4 or 1 − B < 1/4

(d) 3B2 < B

Step 1

For the provided information, the uniform distribution is *B*~*U*(*a*, *b*).

Here *a*=0 and *b*=1. The probability density function for uniform distribution is

*f*(*x*)=1/*b*-*a*.

a. The required probability for 1/3<B<2/3 can be obtained as:

Step 2

b. The required probability for |B-1/2|≤1/4 can be obtained as:

Step 3

c. The required probability for *B* < 1/4 or 1 &minus...

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