Question

Let X have the distribution that has the following probability density function: f(x)={2x,0<x<1        {0, Otherwise...

Let X have the distribution that has the following probability density function:

f(x)={2x,0<x<1
       {0, Otherwise

Find the probability that X>0.5.

Why is the probability 0.75 and not 0.5?

Math   Statistics-And-Probability   
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Answer #1

Since, f(x) is not uniformly distributed, if f(x) would be a constant then probability would be exactly half. But here f(x) = 2x, it depends on x. Larger the value of x, denser will be it it’s density. So P( x > 0.5) obviously be greater than P( x < 0.5). Exact value of P(x > 0.5) = 0.75 which can be found using integration.

Please let me know if you need any further explanation. Thank you

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