Math Answers

Discrete random variables

Find the scalar x- and y-components of the following displacements in the XY-plane: (a) 300 cm at 127° and (b) 500 cm at 220°

1. Show, by the use of the truth table/matrix, that the statement 

(P ⇒ Q) ⇔ (!Q ⇒ !P) is a tautology.

1. Show that P ⇔ Q ≡ (P ^ Q) v (!P ^ !Q) are logically equivalent.

A population consists of the numbers 5, 7, 9,

11, 12, and 15. List all possible sample size of

2 from this population and give the following:

•A. Determine the number of sets of all possible random samples that

can be drawn from the given population.

• B. List all possible samples and compute the mean of each sample.

• C. Construct the sampling distribution.

•D. Construct a histogram of the sampling distribution of the means.

two balls are drawn in succession without replacement from a jar containing 7 red balls and 6 blue balls. Let B be the random variable representing the number of blue balls. Find the mean.

A store donated a lot of 8 computer sets that includes 3 which are malfunctioning or defective. If 4 of this computer sets are chosen at random for delivery to a school.

i) What will be the probability mass function of a random variable 𝑌?

ii) What will be the expected value of 𝑌?

Find the simple interest gained by €2000 over 4 years at 6% annual interest

Three airlines serve a Srinagar. Airline 'Amira' has 50% of all the scheduled flights, airline 'Biyas' has30% and airline 'chinar' has the remaining 20%. Their on-time rates are 80%, 65%, and 40%, respectively.

Part 2) A plane has just left on time. What is the probability that it was airline 'Amira'.

Raggs Limited, a clothing firm, determines that the revenue, in rand, of selling x dresses is given by the function R(x) = x(450 − 0,050x). It also determines that the total cost, in rand, of producing x dresses is given by the function C(x) = 40 000 + 0,025x2. The marginal profit when x dresses are produced and sold, is given by the function

The average height of students in a freshman class of a certain school has been 165.24 cm with a population standard deviation of 5.56 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 37 students in the present freshman class has an average height of 169.42 cm? Use a 0.01 level of significance.