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Nataliya [291]
3 years ago
12

Why do the inequality signs stay the same in the last two steps of exercise 1

Mathematics
2 answers:
MrRissso [65]3 years ago
7 0
The only reason an inequality would change would be because a number is divided or multiplied by a negative number. So if it stayed the same, then it would be because there was no division or multiplication by a negative number. Hope I helped :)
nadya68 [22]3 years ago
6 0
The inequality signs stay the same when you multiply or divide a positive number

They only flip if you multiply or divide a negative number (that is in the divisor place)

hope this helps
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The directions of travel are at right angles to each other, so the Pythagorean theorem can be used to find the straight-line distance to the starting point. That distance (d) satisfies ...

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The appropriate choice is ...

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From the given density function we find the distribution function,

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(a)

F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)

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(b)

F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y

\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2

\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}

(c)

F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})

\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3

\implies f_{U_3}(u_3}=\begin{cases}\frac32\sqrt u&\text{for }0\le u\le1\\0&\text{otherwise}\end{cases}

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