Math Answers

Verify whether f(x) = (8/7) (1/2)^x

, x = 1,2,3 is a probability mass function. If it is,

determine the following probabilities.

(a) P(X ≤ 1)

(b)P(X > 1)

(c) P(2 < X < 6)

(d)P(X ≤ 1 or X > 1)

Test for exactness and find the complete solution of y/(x-1) dx+ {ln(2x-2)+ 1/y}dy=0

Below is an incomplete probability distribution for a random variable X.

x 1 2 3 4 5 6

f(x) 0.15 0.25 0.33 0.09

(a) If f(4) = P(X = 4) = 2P(X = 5), complete the probability distribution above.

(b)Construct a probability histogram of this distribution.

(c) Find the cumulative distribution of the random variable X.

(d)Construct a graph of the cumulative distribution.

A company has 7 applicants, three women and four men. Suppose that the 7

applicants are equally qualified and that no preference is given for choosing either

gender. Let X be the random variable described by the number of women chosen to

fill the two positions.

(a) Express the probability distribution of X as a formula in combinatorial

notation.

(b)Find P(X = 1).

(c) Find P(X ≤ 1).

A key ring contains four office keys that are identical in appearance, but only one will

open your office door. Suppose you randomly select one key and try it. If it does not

fit, you randomly select one of the three remaining keys. If it does not fit, you

randomly select one of the last two.

(a) List the elements of the sample space S using the letters H and M for “hit” and

“miss”, respectively.

(b)To each sample point in S, assign a value x of the random variable X representing

the number of keys that you try until you find the one that opens the door.

(c) Calculate the values of P(X = x) and display them in a table.

Wood paneling can be ordered in thickness of 1/16,1/8,1/4, or3/8inch. The random variable

X is the total thickness of paneling in two orders. List the elements in the sample

space.

Specify and sketch the domain of the following function

f(x,y)= (y^2 + x^2) / √(y^2 - x^2)

Identify the following as discrete or continuous random variables.

(a) Q: Total number of points scored in a football game

(b)R: Shelf life of a particular drug

(c) S: Height of the ocean’s tide at a given location

(d)T: Thickness of a hard-bound books

(e) U: Number of aircraft near-collisions in a year

(f) V: Increase in length of life attained by a cancer patient as a result of

chemotherapy

(g) W: Tensile breaking strength (in pounds per square inch) of 1-inch diameter steel

cable

(h)X: Number of drivers killed in vehicular accidents in a certain locality

(i) Y: Number of overdue accounts in a department store at a particular time.

(j) Z: Your blood pressure

y′′+ 4y= sin 5x+x−1

Q2. Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

7x1 + 9x2 ≥ 300

5x1 + 3x2 ≤ 1500

7x1 + 9x2 ≤ 1900

2x1 + 4x2 ≤ 1000

x1, x2 ≥ 0

-Find graphically the feasible region and the optimal solution.