Discrete Mathematics

Continuous Random Variables

Continuous Random Variables - Probability Density Function (PDF)

         

If the probability density function of a continuous random variable X[1,7]X\in[-1,7] is given by f(x)=a(x+1)(x7),f(x)=a(x+1)(x-7), what is P(0X4)?P(0\le X\le4)?

The probability density function of a continuous random variable XX that ranges from 1 to e2e^{2} is given by f(x)=12x.f(x)=\frac{1}{2x}. Find the value of kk such that P(X>k)=110.P(X>k)=\frac{1}{10}.

If the probability density function of a continuous random variable XX is given by f(x)={ax2 (0x1)a9(x1)+a (1<x10),f(x)=\begin{cases} ax^2\ &(0\le x\le1) \\-\frac{a}{9}(x-1)+a\ &(1<x\le10),\end{cases} what is the value of a?a?

If the probability density function of a continuous random variable X[0,π16]X\in[0,\frac{\pi}{16}] is given by f(x)=asin8x,f(x)=a\sin8x, what is the variance of XX divided by π3? \pi-3 ?

If the probability density function of a continuous random variable XX is given by f(x)=11x10 (0x1),f(x)=11x^{10}\ (0\le x\le1), what is E[X]?E[X]?

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