Define a term random variable and explain different types of random variable.
[3 marks]Acard is drawn at random from a pack of 52 cards. What is the probability that the card is a spade or a king?
[4 marks]State Baye’s theorem. There are three bags; first containing 1 white, 2 red and 3green balls; second 2 white, 3 red and 1green balls and third 3 white, 1 red and 2 green balls. Two balls are drawn from a beg chosen at random. These are found to be 1 white and 1 red. Find the probability that the balls so drawn came from the second bag.
[7 marks]Two judges in a beauty contest rank the 12 contestants as follows: x 1 2 3 4 5 6 7 8 9 10 11 y 12 9 6 10 3 5 4 7 6 2 11 1 Calculate rank correlation coefficient.
[12 marks]Abook contains 100 misprints distributed randomly throughout its 100 pages. What is the probability that a page observed at random contains at least misprints.
[2 marks]Adie is thrown six times. If getting an odd number is a success, find the probability of (i) 5 success (ii) at least five success and (iii) at most five success.
[7 marks]If a random variable x is Gamma distribution with parameter 𝜆 = 3, compute the value of (i) P(x≤1) and (ii) P(1≤x≤2).
[7 marks]Calculate the coefficient of variance for the following data: Class 0-10 10-20 20-30 30-40 40-50 Interval Frequency 5 7 2 3
[3 marks]Calculate the median for the following data: Class 0-30 30-60 60-90 90-120 120- 150-180 Interval 150 Frequency 8 13 22 27 18
[7 marks]Compute the correlation coefficients between Xand Yusing following data: X 2 4 5 6 8 11 Y 18 12 10 8 7
[5 marks]Obtain correlation coefficient between x and y if two regression lines are 4x- 5y+33=0 and 20x-9y-107=0.1
[3 marks]Calculate the mode for the following data: Class 0-10 10-20 20-30 30-40 40-50 Interval Frequency 10 14 19 7 13
[4 marks]Obtain the regression line of y on x for the following data: x 100 98 78 85 110 93 80 y 85 90 70 72 95 81 74
[7 marks]Explain the term related to testing of hypothesis: (i) Null hypothesis (ii) Alternate hypothesis and (iii) Errors while accepting or rejecting a hypothesis.
[3 marks]The mean of 35 sample of the thermal conductivity of a certain kind of cement brick is 0.343 with standard deviation of 0.010. Test the hypothesis that the population mean is 0.340 at 5% level of significance.
[4 marks]Fit a binomial distribution for the following data showing the survey of 800 families with 4 children and test the goodness of fit. No. of boys 0 1 2 3 No. of girls 4 3 2 1 0 No. of families 32 178 290 238 64
[4 marks]Arandom sample of size 15 from bivariate normal distribution gave a correlation coefficient r=0.5. Is this indicate the existence of correlation in the population?
[3 marks]Atire company is suspicious to claim that the average lifetime of certain tires is at least 28000 km. To check the claim, the company takes the sample of 40 tires and gets a mean life time of 27463 km with standard deviation of 1348 km. Test the hypothesis at 1% level of significance.
[4 marks]Fit a Poisson distribution for the following data and test the goodness of fit. x 0 1 2 3 f 112 73 30 4 1
In y = a +bx if ∑x = 50, ∑y = 80, ∑xy = 1030,∑x2 = 750 and n = 10, then find a and b.
[3 marks]Fit a curve y = aebx for the following data: x 1 2 3 y 7 11 17 27
[4 marks]State properties of the normal distribution. Suppose the marks of 800 students are normally distributed with mean 66 and standard deviation 5. Find number of students getting marks (i) between 65 and 70 (ii) greater than or equal to 72 (Given that P(0≤z≤0.20)=0.0793, that P(0≤z≤0.80)=0.2881 and that P(0≤z≤1.2)=0.3849)
[7 marks]Arandom variable x has the following probability distribution: x 0 1 2 i p 1/6 3/8 3/8 1/8 i Find the standard deviation of x for the given distribution.
[3 marks]With usual notations, find the value of p for a binomial random variable x when n=6 and 9P(x=4)=P(x=2).
[4 marks]Fit a parabola y = ax2 +bx+c for the following data: x -1 0 1 y -2 1 2
[4 marks]