Math Answers

1. Determine whether these functions are onto, one-to-one, both or neither. Justify your answer.

a)   f(1) = c, f(2) = d, f(3) = a, f(4) = d, f(5) = b

b)   g(1) = d, g(2) = c, g(3) = a, g(4) = b

c)   h(1) = b, h(2) = d, h(3) = b, h(4) = c

State whether the following statements are true or false and reason for support it

(1) If the level of significance is the same, the area of the rejection region in a two tailed test is less than that in a one tailed test.

(2)Non parametric tests are more powerful than the parametric tests

(3)If T1 and T2 are two estimators of the parameter theta such that varience of T2 =1/n and varience of T2=n then T1 is more efficient than T2

A 95% confidence interval is smaller than 99% confidence interval. State whether the given statement is true or false give reason in support of answer

Prove or disprove that the two propositions in each pair are equivalent.

 ((p "\\leftrightarrow" q) "\\leftrightarrow" r), (p "\\leftrightarrow" (q "\\leftrightarrow" r))

Prove or disprove that the two propositions in each pair are equivalent.

 (p "\\bigoplus" (q "\\to" r)), ((p "\\bigoplus" q) "\\to" (p "\\bigoplus" r))

1.  Prove or disprove that the two propositions in each pair are equivalent.

a)   (p "\\to" (q "\\to" r)) , ((p "\\to" q ) "\\to" ( p "\\to" r ))

A petrol station has two pumps. The service time follows the exponential distribution with mean 4 minutes and cars arrive for service in a Poisson process at the rate of 10 cars per hour. Find the probability that a customer has to wait for service. What proportion of time the pump remains idle?  

a)     A supermarket has two girls ringing up sales at the counters. If the service time for each customer is exponential with mean 4 minutes and if the people arrive in Poisson fashion at the rate of 10 per hour

a)        What is the probability of having to wait for service?                       

 b)       What is the expected percentage of idle time for each girl?              

 c) If a customer has to wait, what is the expected length of his waiting time?

Give the inverse, converse and contrapositive for each of the following propositions.

a) If x + y = 1 then x2 + y2 ≥ 1

b) If 2 + 2 = 4 then 3 + 3 = 8

Determine whether the following are propositions. Give the truth value of the propositions.

a) Asia is the largest of the Earth’s seven continents.

b) 4 + x = 5

c) 2 * 3 = 5

d) Answer this question

e) The human heart is shaped like an upside-down pear and is located slightly to the left of center inside the chest cavity