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labwork [276]
2 years ago
8

HELP, I’M STUCK !

Mathematics
1 answer:
vaieri [72.5K]2 years ago
6 0

Since P(<em>X</em> = <em>x</em>) = 0.3 for all 0 ≤ <em>x</em> ≤ <em>α</em>, we have

\displaystyle\int_{-\infty}^\infty P(X=x)\,\mathrm dx=1\implies0.3\int_0^\alpha\mathrm dx=0.3\alpha=1\implies\alpha=\dfrac{10}3

So,

P(X>2) = \displaystyle\int_2^\infty P(X=x)\,\mathrm dx=0.3\int_2^{\frac{10}3}\mathrm dx

P(X>2)=0.3\left(\dfrac{10}3-2\right)=\boxed{\dfrac25}

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