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$p(x)=3x^2$ with $0 < x < 1$: 0 elsewhere.

$p(x)$ is the probability density function of the variables.

there are 3 independent variables $X_1$,$X_2$,$X_3$ with the distribution listed above

What is the probability exactly 2 are greater than $1/2$?

Thanks!

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    If $p(x)$ is supposed to be the probability density function of each of the three random variables then you should probably say so.2011-09-23

1 Answers 1

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Hint 0: for a continuous random variable $X$ with a probability density function $p(x)$, you have $\Pr(X \le k) = \int_{x=-\infty}^{k} p(x) \; \text{d}x$

Hint 1: Work out $\Pr\left(X_1 \le \frac{1}{2}\right)$ and $\Pr\left(X_1 \gt \frac{1}{2}\right)$; the same will apply to $X_2$ and $X_3$ as they have identical distributions

Hint 2: As they are independent and identical, treat the question as finding the probability of getting exactly two success from three in a binomial distribution

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    @Dilip Sarwate: Yes, thank yo$u$, I can't integrate.2011-09-24