Allow X to signify the voltage at the yield of a mouthpiece, and assume that X has a uniform circulation on the stretch from ?1 to 1. The voltage is handled by a "hard limiter" with cutoff esteems ?0.5 and 0.5, so the limiter yield is an arbitrary variable Y identified with X by Y = X if |X| ? 0.5, Y = 0.5 if X > 0.5, and Y = ?0.5 if X

(a) What is P(Y = 0.5)?

(b) Obtain the combined appropriation capacity of Y.

If it's not too much trouble, show your work, much obliged!

A firm uses pattern projection and occasional components to reproduce deals for a given time frame period. It doles out "0" if deals fall, "1" if deals are consistent, "2" if deals rise reasonably, and "3" if deals rise a ton. The test system creates the accompanying yield.

0 1 0 2 0 1 0 3 2 0 2 1 2 3 1 2 0 2 0 3 0 2 1 0 1

Gauge the likelihood that deals will rise tolerably.

a

0.258

b

0.233

c

0.312

@2@

d

0.226

Consider the examination of flipping a reasonable coin until two heads or two tails show up in

progression.

(a) Describe the example space.

(b) What is the likelihood that the analysis closes before the 6th throw?

(c) What is the likelihood that the investigation closes after a much number of throws?

(d) Given that the examination closes with two heads, what is the likelihood that the

analyze closes before the 6th throw?

(e) Given that the investigation doesn't end before the third throw, what is the likelihood that

the analysis doesn't end after the 6th throw?

Allow X to mean the measure of time a book on two-hour hold is really looked at, and assume the cdf is the accompanying. F(x) = 0 if x = 5. Utilize the cdf to acquire the accompanying. (On the off chance that vital, round your response to four decimal spots.)

(g) Calculate V(X) and ?x.

(h) If the borrower is charged a sum h(X) = X2 when checkout length is X, figure the normal charge E[h(X)].

2. Find the p-value for the following hypothesis tests a) Ho: H = 10 vs HA: H > 10 with test stat t20 = 2.37 b) Ho: H = 10 vs HA: H