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A certain store has four ways of handling returns: cash refund, credit to account, exchange, or refusal. The manager claims that the four ways are equally probable to test this hypothesis, 108 customers were sampled with the following results
Type Cash Credit exchange Refusal
Count 34 27. 32 15
Does the data support the managers claim at 5 %. (6mks)
(a) Find the derivative of the function π¦ = 2π₯^2+12/x^2, when π₯ = 2.
(b) Let π(π₯) = β3/π₯β7. Find the inverse of the function.
The proportion of eligible voters in the next corporation election (in tumkur) who will voteΒ
for the incumbent is assumed to be 55%. What is the probability that in a random sample ofΒ
500 voters less than 49% say they will vote for the incumbent? Write your conclusion.Β
The diameter , Say X , of a electric cable , is assumed to be continuous random variable with p.d.f : f(x)= 6x(1-x) , 0<=x<=1.
(1) Check that the above is a P.D.F.
(2) Obtain an expression for the c. d. f. of X.
(3) Compute P(X<=1/2| 1/3<=X<=2/3), and
(4) Determine the value of k such that P(X<k)=P(X>k).
Question 6 [2]
State the mean Value Theorem.
Question 5 [2;2]
Investigate whether the following functions are odd or even.
(a) π(π₯) = π₯^
3
(b) π(π₯) = cos π₯
A mainframe computer has 4 ports. At any given time each port is either in use or not in use. How many possibilities are therefore overall port usage of this computer? Determine possible outcomes of at least two ports
Question 4 [7]
Prove that π(π₯) = π₯^2 + 2π₯ is not injective.
Question 2 [7]
Use sign table to determine the values of π₯ for which
x^2 + 9π₯ + 20 β€ 0.
Consider the relation π = {(1,7), (β1,7), (3,9), (1,3)}. Is π a function? Justify
your answer
