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.

**Q2: **

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

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**Q3: **

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

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**Q4: **

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

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**Q5: **

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

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**Q6: **

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

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**Q7: **

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

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**Q8: **

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

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**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 .

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**Q11: **

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

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**Q12: **

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

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**Q13: **

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

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**Q14: **

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

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**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 .

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**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 .

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**Q20: **

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

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**Q21: **

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

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**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 .