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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 𝑋 be a continuous random variable with probability density function 𝑓(𝑥)=4𝑥+𝑘213≤𝑥≤4,0.ifotherwise Find the value of 𝑘.

Q2:

Let 𝑋 be a continuous random variable with the probability density function 𝑓(𝑥)=⎧⎪⎨⎪⎩𝑥82<𝑥<3,1483<𝑥<36,0.ififotherwise Find 𝑃(11≤𝑥≤24).

Q3:

Let 𝑋 be a continuous random variable with probability density function 𝑓(𝑥)=18(6𝑥−7)2≤𝑥≤3,0.ifotherwise Find 𝑃(2≤𝑋≤2.5).

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