3. There are three surviving members of the Jones family: John, Sarah, and

Beatrice. All live in different locations. The probability that each of these

three family members will have a stay of some length in the hospital next

year is 0.2.

a) What is the probability that none of the three of them will have a

hospital stay next year? (.512)

b) What is the probability that all of them will have a hospital stay next

year?

c) What is the probability that two members of the family will spend

time in hospital next year? (.096)

d) What is the probability that either John or Sarah, but not both, will

spend time in the hospital next year?

The grouping of particles in a suspension is 50 for each mL. A 5 mL volume of the

suspension is removed.

a. What is the likelihood that the quantity of particles removed will be among 235 and

265?

b. What is the likelihood that the normal number of particles per mL in the pull out example

is somewhere in the range of 48 and 52?

c. In the event that a 10 mL test is removed, what is the likelihood that the normal number per mL

of particles in the removed example is somewhere in the range of 48 and 52?

d. How huge an example should be removed with the goal that the normal number of particles per mL in

the example is somewhere in the range of 48 and 52 with likelihood 95%?

In an arbitrary example of 100 batteries created by a specific technique, the normal

lifetime was 150 hours and the standard deviation was 25 hours.

(I) Find a 95% certainty span for the mean lifetime of batteries created by this

model.

(ii) Find a 99% certainty span for the mean lifetime of batteries created by this

model.

(iii) A designer asserts that the mean lifetime is somewhere in the range of 147 and 153 hours. With what

level of certainty can this assertion is made?

(iv) Approximately the number of batteries should be inspected with the goal that a 95% certainty

stretch will indicate the intend to inside 2 hours?

(v) Approximately the number of batteries should be examined so a 99% certainty

stretch will determine the intend to inside 2 hours

A Company scientist has been given the assignment of gathering data pretty much all representatives

inside the organization to more readily comprehend the adequacy of their advanced education pathway

program offered to all representatives. The likelihood that a worker has been at the organization

at least five years is 0.74, the likelihood that a representative has a Master's level certificate or

higher is 0.34, and the likelihood that an arbitrarily chosen worker has been at the organization

at least five years and has a Master's certificate is 0.12.

F. Of the individuals who have a graduate degree 35.29% have been at the organization at least 5 years

while those with lower degrees 93.94 % have been at the organization at least 5 years. Make a likelihood tree portraying the present circumstance.

Thank you kindly for responding to me. Would you be able to kindly answer the (iv) and (v) sub parts.

In an irregular example of 100 batteries delivered by a specific strategy, the normal

lifetime was 150 hours and the standard deviation was 25 hours.

(I) Find a 95% certainty span for the mean lifetime of batteries created by this

model.

(ii) Find a 99% certainty span for the mean lifetime of batteries created by this

model.

i21i

(iii) An architect guarantees that the mean lifetime is somewhere in the range of 147 and 153 hours. With what

level of certainty can this assertion is made?

(iv) Approximately the number of batteries should be tested with the goal that a 95% certainty

span will determine the intend to inside 2 hours?

(v) Approximately the number of batteries should be tested with the goal that a 99% certainty

span will determine the intend to inside 2 hours?

Question 2 1 pts 2. Let the joint probability density function of x and y be fxy (x, y) = C 0 0. (a) Find the value of k. (b) Find the joint cumulative distribution function of X and Y. (c) Find P(0 1). (d) Find and sketch the marginal pdf of X. (e) Determine the value of d that minimizes E[(X - d)2] and E[X - dl]. (f) Find the variance of 2X - Y. (g) Find the pdf of W = X2.Let X1 and X3 be two independent random variablea with uniform distribu- tion on [[3, 1]. 1. Write down the joint cumulative distribution function and joint probability density function ole + X; and X11}. 2. Write down the covariance between X1 + X; and X14353. 3. Let 2' be the largest magnitude {absolute value] of a root of the equation a\" X12 + X: = II]. Let A be the random event which says that the equation :2 X12; + X: = [i has no real roots. Find the conditional e.d.f. of 3 when A is true