Mathematics, 23.08.2019 00:10 Jennifer2019

3) the length of time to failure (in hundreds of hours) for a transistor is a random variable y with distribution function give by f(y) = 0, y < 0 1 − e −y 2 , y ≥ 0 a) show that f(y) has the properties of a distribution function. b) find f(y). c) find the probability that the transistor operates at least 200 hours.

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Answer from: thompsonjodi9638

Looks like

$F(y)=\begin{cases}0&\text{for }y$

a. F(y) is a valid distribution function if

$F(y)\to0$ as $y\to-\infty$ ; $F(y)\to1$ as $y\to+\infty$ ; F(y)

is non-decreasing; and F(y)

is "right-continuous", meaning that the limit of any "piece" of F(y)

as $y\to c$ from the right exists.

The first two conditions are met: we have

$\displaystyle\lim_{y\to-\infty}F(y)=0$

$\displaystyle\lim_{y\to+\infty}F(y)=\lim_{y\to+\infty}(1-e^{-y^2})=1$

The second condition is also met:

$F'(y)=\begin{cases}0&\text{for }y0\end{cases}$

both of which are non-negative over their respective domains.

Finally, the fourth condition is met because F(y) is continuous everywhere.

b. We already found f(y) above when checking for the monotonicity of F(y) ; the probability density f(y) is simply the derivative of the distribution function F(y) .

$f(y)=F'(y)=\begin{cases}0&\text{for }y$

(Notice that we include y=0 so that the P(Y=0) exists.)

c. By definition of the distribution function, we have

$P(Y\ge200)=1-P(Y$

which is value very close to 0.

Answer from: Quest

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes.

step-by-step explanation:

Answer from: Quest

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

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