Math Answers

a) Consider the whole of the English words set. Suppose an English word x is related to another

English word y if x and y begin with the same letter.

i) Show that this is an equivalence relation.

ii) Compute C(quadratic) and C(rhombus)

iii) How many equivalence classes are there in all, and why?

iv) What is the partition of the English words under this relation?

b) Consider Z, the set of integers. Suppose we define the relation: x is related to y if x - y > 3, x, y \in Z. Determine whether or not the relation is

i) reflexive

ii) symmetric

iii) transitive

1 4 4 2 3 4 5 1 4 1

Work out the mode

Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 0 when X = 1 and Y = 1 when X = 0. What is the mean and variance of X + Y?

Let X be a binomial(5, 0.2) random variable. Let Y be a discrete random variable that is independent of X, such that Y = 1 with probability 0.2 and Y = 0 with probability 0.8. What is the probability that the sum of X and Y is less than or equal to 3?

A sum of 45000 invested will provide payments of 500 each at the end of every 2 months for 7 years find the under lying rate of interest compounded semi annualy

To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4

with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.)

a) Test, at

  0.05

, whether the difference is significant or not.

b) Test if the difference is 3.0.

To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4

with Sd. of 5.0, and 50 girls averaged 62.8 with Sd. of 4.6. (Group Assignment) (2 pts.)

a) Test, at

  0.05

, whether the difference is significant or not.

b) Test if the difference is 3.0.

How much was borrowed if a simple interest rate of 7.5% was offered payable in 12 months with interest of ₱105.00?

Oranges chosen at random have a mean mass of 210 grams and standard deviation of 35 grams. Assuming a normal distribution, what is the probability of choosing an orange with a mass between 170 grams and 250 grams

The force of interest δ(t) is a function of time and, at any time t (measured in years),

is given by the formula:

δ(t) =



0.07 0.005t , 0 t < 5

0.06 0.003t, 5 t < 10

0.03, t > 10

(a) Calculate the accumulated amount at time t = 15 of $100 invested at time

t = 0.