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21. Random numbers Let Xbe a number between 0and 1produced by a random number generator. Assuming that the random variable X has a uniform distribution, find the following probabilities:
(a) P(X>0.49)
(b) P(X0.49)
(c) P(0.19X<0.37or0.84<X1.27)

Short Answer

Expert verified

(a) The probability for P(X>0.49)is 0.51.

(b) The probability for P(X0.49)is 0.51.

(c) The probability for P(0.19X<0.37or0.84<X1.27)is 0.34.

Step by step solution

01

Part (a) Step 1: Given information 

Given in the question that, Consider Xas a number between 0and 1created by a random number generator.

We have to And to find the probability for P(X>0.49).

02

Part (a) Step 2: Explanation

The variableX has the uniform distribution.
Therefore, the value of P(X>0.49)by:

P(X>0.49)=(10.49)1=0.51

03

Part (b) Step 1: Given information 

Let Xbe a number between 0and 1produced by a random number generator.

We have to find the probability for P(X0.49).

04

Part (b) Step 2: Explanation 

The variable Xhas the uniform distribution.

Therefore, the value of P(X0.49)will be:

P(X0.49)=(1-0.49)1=0.51

05

Part (c) Step 1: Given information 

Let Xbe a number between 0and 1 produced by a random number generator.

We have to find the probability for P(0.19X<0.37or0.84<X1.27).

06

Part (c) Step 2: Explanation 

Since, the probability forP(0.19X<0.37or0.84<X1.27)can determine as:
P(0.19X<0.37)=(0.37-0.19)1=0.18
P(0.84<X1.27)=(1-0.84)1=0.16

Then,

P(0.19X<0.37)=0.18+0.16=0.34orP(0.84<X1.27)=0.18+0.16=0.34

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