A fair die is tossed. If the resulting number is even, you add 1 to your score and get that many rupees. If the resulting number is odd, you add 2 to your score and get that many rupees. If X denotes the random variable counting your gain in rupees, then write probability distribution of X.
See Answer →There are three coins in a box. When tossed, one of the coins comes up heads only 30% of the time, one of the coins is fair, and the third comes up heads 80% of the time. A coin is selected at random from the box and tossed three times. If two heads and a tail come up in this order (HHT) what is the probability that the coin was the fair coin?
See Answer →An urn contains 10 white marbles, 15 blue marbles, and 20 red marbles. Five marbles are selected, one at a time, with replacement. Find the probability that at least one color will be missing from the 10 selected marbles
See Answer →Roll two fair dice, one red and one blue, and consider the events:
A: “The red die lands on 4”,
B: “The sum on the dice is 9” and
C: “The blue die lands on an odd number”.
Determine which pairs of events are independent.
See Answer →If a random variable X may assume values then it cannot be discrete random variable
If X is a continuous random variable then
If standard deviation of a random variable X is 3 and Y = -5X -10 then SD(Y) = -85.
See Answer →Two cards are drawn one at a time from a 52-card standard deck. Then the probability that the second card is red, if the drawing is done with replacement is 1/2
See Answer →State whether the following statements are True or False and also give the reason in support of your answer.
(a) If odds in favour of an event A are 3:5 then odds against of the event A will be 5:3.
(d) If X denotes the waiting time in minutes until the 3rd customer arrives in a mobile showroom, then X follows exponential distribution.
(e) The probability that a shooter hits a target in Olympic is 1/3. If she fires 6 times, then to calculate the probability of hitting the target at least 3 times we can use geometric distribution.
See Answer →Investigate the association between darkness of eye-colour in father and son from the following data:
Fathers with dark eyes and sons with dark eyes: 50
Fathers with dark eyes and sons with not dark eyes: 79
Fathers with not dark eyes and sons with dark eyes: 89
Fathers with not dark eyes and sons with not dark eyes: 782
Also tabulate for comparison the frequencies that would have been observed had there been no heredity.
See Answer →An investigation of 23,713 households was made in an urban and rual mixed locality. Of these 1,618 were farmers, 2,015 well-to-do and 770 families were having at least one graduate. Of these graduate families 335 were those of farmers and 428 were well-to-do, also 587 well-to-do families were those of farmers and out of them only 156 were having at least one of their family member as graduate. Obtain all the ultimate class frequencies
See Answer →An individual purchases three qualities of pencils. The relevant data are given below.
| Quality | Price per pencil (Rs.) | Money spent (Rs.) |
| A B C | 1.00 1.50 2.00 | 50 30 20 |
Calculate the average price per pencil.
See Answer →The following table gives, according to age, the frequency of marks obtained by 100 students in an intelligence test:
| Age in years → Marks | 18 | 19 | 20 | 21 | Total |
| 10–20 20–30 30–40 40–50 50–60 60–70 | 4 5 6 4 – –
| 2 4 8 4 2 2 | 2 6 10 6 4 3 | – 4 11 8 4 1 | 8 19 35 22 10 6 |
| Total | 19 | 22 | 31 | 28 | 100 |
Calculate the Coefficient of Correlation between the Age and Marks.
See Answer →Fit an exponential curve of the from Y = abX to the following data:
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Y | 1.0 | 1.2 | 1.8 | 2.5 | 3.6 | 4.7 | 6.6 | 9.1 |
In a partially destroyed laboratory, record of an analysis of correlation data, the following results only are legible: Variance of X = 9. Regression equations: 8X – 10Y + 66 = 0, 40X – 18Y = 214. What are: (a) the mean values X and Y, (ii) the correlation coefficient between X and Y, and (iii) the standard deviation of Y?
See Answer →Calculate the first four moments of the following distribution about the mean and hence find β1 and β2.
| X; | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| F: | 1 | 8 | 28 | 56 | 70 | 56 | 28 | 8 | 1 |
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The mean and the standard deviation of a characteristic of 100 items were found to be 60 and 10 respectively. At the time of calculations, two items were wrongly taken as 5 and 45 instead of 30 and 20. Calculate the corrected mean and corrected standard deviation.
See Answer →Compute coefficient of variation for factory A and B from the following:
| Daily Wages (Rs.) : | 12 | 15 | 17 | 22 | 25 | 30 |
| Workers in Factory A: | 5 | 10 | 20 | 35 | 12 | 8 |
| Workers in Factory B: | 15 | 25 | 30 | 35 | 21 | 19 |
Find: (i) Which factory pays higher average daily wages? (ii) In which factory are wages more variable?
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If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated
See Answer →The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively
See Answer →The correlation coefficient between x and (a – x) is –1.
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