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Chapter 5: Q.5.10 (page 346)

f(x)for a continuous probability function is15 , and the function is restricted to 0鈮�x鈮�5. What is P(x<0)?

Short Answer

Expert verified

The value of theP(x<0)iszero.

Step by step solution

01

Given information

f(x)for a continuous probability function is 15

The function is restricted to0鈮�x鈮�5

02

Solution

Here, the probability density function of the continuous random variable Xis defined as:

f(x)=15,鈥呪赌呪赌呪赌�0鈮�x鈮�50,鈥呪赌呪赌呪赌�otherwise

So, the probability value of P(x<0)will be calculated as:

P(x<0)=1鈭�P(x鈮�0)

=1鈭�鈭�05鈥�15dx

=1鈭�15[x]05

=1鈭�15[5鈭�0]

=0

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