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In this lesson, we will learn how to describe the probability density function of a continuous random variable and use it to find the probability for some event.

Q1:

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

Q2:

Let π be a continuous random variable with the probability density function Find π ( 1 1 β€ π₯ β€ 2 4 ) .

Q3:

Let π be a continuous random variable with the probability density function Find π ( 1 4 β€ π₯ β€ 1 5 ) .

Q4:

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

Q5:

Let π be a continuous random variable with probability density function Find π ( π β€ 8 ) .

Q6:

Let π be a continuous random variable with probability density function Find π ( 3 0 . 5 β€ π₯ β€ 3 1 . 5 ) .

Q7:

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

Q8:

Let π be a standard normal random variable. Determine π , given that π ( β 2 . 9 8 β€ π β€ π ) = 0 . 7 0 7 4 .

Q9:

Let π be a continuous random variable with probability density function Find π ( π > 4 ) .

Q10:

Q11:

Let π be a continuous random variable with probability density function Find π ( 3 β€ π₯ β€ 4 ) .

Q12:

Let π be a continuous random variable with the probability density function Find π ( π > 6 4 ) .

Q13:

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

Q14:

Q15:

Let π be a continuous random variable with probability density function Find π ( 4 . 5 β€ π β€ 7 ) .

Q16:

Let π be a continuous random variable with probability density function Given π ( π β€ π β€ π + 2 ) = 5 1 2 and π β [ 2 , 6 ] , determine the value of π .

Q17:

Q18:

Calculate the probability density function at π₯ = 1 for an exponential distribution with π = 1 .

Q19:

Let π be a continuous random variable with probability density function Given π ( π β€ π ) = 7 1 1 4 8 and π β [ 3 , 4 ] , determine the value π .

Q20:

Let π be a continuous random variable with probability density function Find π ( π > 4 . 5 ) .

Q21:

Let π be a continuous random variable with probability density function Given that π ( 1 3 < π < π ) = 1 3 5 0 , find the value of π .

Q22:

Let π be a continuous random variable with the probability density function Find π ( 2 β€ π₯ β€ 2 . 5 ) .

Q23:

Suppose that π is a standard normal random variable. Given that π ( π β₯ π ) = 0 . 4 4 8 3 , find π using the standard normal distribution table.

Q24:

Let π be a continuous random variable with probability density function Find π ( π = 3 7 ) .

Q25:

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

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