The continuous random variable X has probability density function (a) Find k. (b) Find the mean. (c) Find the variance.
Added by Justin S.
Step 1
We know that the total probability of a probability density function is 1. So, we can set up the following integral: $$ \int_{0}^{3} k(3-x)dx = 1 $$ Now, we can solve for k: $$ k \int_{0}^{3} (3-x)dx = 1 \\ k \left[3x - \frac{1}{2}x^2\right]_0^3 = 1 \\ k Show more…
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