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The probability density function of a given random variable is given by the graph below. How can I set up the integral in order to find P(X>0, P(X>3/4).

I tried to set up the integral and this is my attempt.

For the P(X>0, P(X>3/4), I have set the integral as From zero until 1/2. The first picture is from 0 until 0.5(1/2) and the second is from 0.5 until 3/4. From 1/2 until 1

Vinicius L. Beserra
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1 Answers1

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Hint:

The pdf is

$$f_X(x)=\begin{cases} 0.5, \ \ -0.5 < x \leq 0.5 \\ 1 , \ \ 0.5 < x \leq 1 \\ 0 \ \ \ \ \text{elsewhere} \end{cases}$$

Thus $P(X>0,X>3/4)=P(X>3/4)=\int_{3/4}^1 1 \, dx$

It is comprehensible ? Can you go on, without using wolfram alpha ?

callculus42
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  • What does the comma mean in this case? – Vinicius L. Beserra Jul 03 '16 at 23:28
  • @ViniciusL.Beserra $P(X>0,X>3/4)$ has the same meaning as $P(X>0 \cap X>3)$ It is the intersection. Thus $X$ is greater $0$ and greater $3$ It is obvious that the condition $X>0$ is redundant. If it is not obvious then have a look on a number line. – callculus42 Jul 04 '16 at 01:35