# Worksheet: Continuous Random Variables

In this worksheet, we will practice describing the probability density function of a continuous random variable and using it to find the probability for some event.

Q1:

Let be a continuous random variable with probability density function Find the value of .

Q2:

Let be a continuous random variable with the probability density function Find .

• A
• B7
• C
• D

Q3:

Let be a continuous random variable with probability density function Find .

• A0
• B
• C
• D

Q4:

Let be a continuous random variable with probability density function Find .

• A
• B
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• D0

Q5:

Let be a continuous random variable with probability density function Find .

• A
• B
• C
• D

Q6:

Let be a continuous random variable with probability density function Find .

• A
• B
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• D

Q7:

Let be a continuous random variable with probability density function Find .

• A
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• D

Q8:

Let be a continuous random variable with the probability density function Find the value of .

• A
• B
• C
• D10

Q9:

Let be a continuous random variable with probability density function Find the value of .

Q10:

Let be a continuous random variable with probability density function Find .

• A
• B
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• D

Q11:

Let be a continuous random variable with the probability density function Find .

• A
• B
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• D

Q12:

Let be a continuous random variable with probability density function Determine the value of .

• A12
• B
• C
• D

Q13:

Let be a continuous random variable with probability density function Find the value of .

• A4
• B
• C
• D

Q14:

Let be a continuous random variable with probability density function Find .

• A
• B1
• C
• D

Q15:

Let be a continuous random variable with probability density function Given and , determine the value of .

Q16:

Let be a continuous random variable with probability density function Given and , determine the value .

Q17:

Let be a continuous random variable with probability density function Find .

• A
• B
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• D

Q18:

Let be a continuous random variable with probability density function Given that , find the value of .

Q19:

Let be a continuous random variable with the probability density function Find .

• A
• B0
• C
• D

Q20:

Let be a continuous random variable with probability density function Find .

• A
• B
• C
• D

Q21:

Let be a continuous random variable with probability density function Find the value of .

• A
• B
• C
• D

Q22:

Calculate the probability density function at for an exponential distribution with .

Q23:

Let be a standard normal random variable. Determine , given that .

Q24:

Suppose that is a standard normal random variable. Given that , find using the standard normal distribution table.

Q25:

Suppose is a standard normal random variable. Given , find the value of .