A random 5-card poker hand is dealt from a standard deck of cards. Find the probability (in terms of binomial coefficients) of getting a flush (all 5 cards being of the same suit: do not count a royal flush, which is a flush with an ace, king, queen, jack and 10).
See Answer →There are 4 black, 3 blue and 8 red balls in an urn. Three balls are selected one by one without replacement. What is the probability that:
(i) First ball drawn is black, second one is red and third one is blue.
(ii) All the three balls are of the same colour.
See Answer →(a) Sample space of a (i) random experiment tossing two coins simultaneously and (ii) One coin two times is the same .
(b) Standard deviation of a random variable X may take any real value, i.e. its value lies in the interval (− ∞ , ∞ ).
(c) If events E1 , E2 , E3 , E4 , ...., En are mutually exclusive and exhaustive then P(E1 ∪ E2 ∪ E3 ∪ .... ∪ En ) will be greater than 1/2 but less than 1.
(d) If S is sample space of a random experiment and E is an event defined on this sample space then P(S|E) = 1.
(e) If X is a random variable having range set {0, 1, 2, 3} then the set {x ∈ S: X(x) = 0} is an event having at least one outcome of the random experiment.
See Answer →State whether the following statements are True or False and also give the reason in support of your answer. (5×2=10)
(a) Sample space of a (i) random experiment tossing two coins simultaneously and (ii) One coin two times is the same.
(b) Standard deviation of a random variable X may take any real value, i.e. its value lies in the interval.[- ∞ , ∞ ]
See Answer →In the given data, two frequencies are missing and its mean is found to be 1.46.
| No. of Accidents (x) | Frequencies (f ) |
| 0 | 46 |
| 1 | ? |
| 2 | ? |
| 3 | 25 |
| 4 | 10 |
| 5 | 5 |
| Total | 200 |
Find the missing frequencies.
See Answer →50% of items have characteristics A and B both, 35% have A, but not B, 25% have B but not A. Show that there must be some misprints in this report.
See Answer →Suppose X and Y are the two variables having the correlation coefficient 0.85. The following are the values they have:
| X | Y |
| 10 | 40 |
| 30 | 30 |
| 50 | 70 |
| 60 | 80 |
If two new variables X' and Y' are obtained by adding 50 to each value of X and 100 to each value of Y, respectively, calculate the correlation coefficient between X' and Y' using the above data. Also compare the results.
See Answer →In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as 8X - 10Y + 70 = 0 and 20X - 9Y - 65 = 0. The standard deviation of X = 3, then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y.
See Answer →Can vaccination be regarded as a preventive measure for smallpox from the given data:
(i) Of 1482 persons in a locality exposed to smallpox, 368 in all were attacked, and
(ii) Of 1482 persons, 343 had been vaccinated and of these only 35 were attacked.
See Answer →An investigation of 23713 households was made in an urban and rural mixed locality. Of these 1618 were farmers, 2015 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 graduate. Obtain all the ultimate class frequencies.
See Answer →Given the following data:
r12 = 0' 8 , r13 = 0.6 and r23= 0.4 then find (i) r12.3 (ii) r13.2 (iii) r23.1 (iv) R1.23
See Answer →The following table shows the information as:
| Statistical Measures | Advertisement Expenditure (X) (Rs. Lakhs) | Sales (Y) (Rs Lakhs) |
| Mean | 20 | 100 |
| Standard Deviation | 30 | 12 |
r(X, Y) = 0.8. Then find
(i) the expected advertising expenditure of the company if sale is Rs. 125 lakhs, and
(ii) the expected sales of the company if the advertising expenditure is Rs 32 lakhs.
See Answer →Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:
The value of Spearman's rank correlation coefficient of a set of non-repeating values was found to be 2/3. The sum of the squares of difference between the corresponding ranks was 55. Find the number of pairs .
See Answer →The following is the distribution of age (in years) of 800 workers:
| Age Group | Age Group |
| 20 — 25 | 50 |
| 25 — 30 | 70 |
| 30 — 35 | 100 |
| 35 — 40 | 180 |
| 40 — 45 | 150 |
| 45 — 50 | 120 |
| 50 — 55 | 70 |
| 55 — 60 | 60 |
Find (i) Median, (ii) Quartile Deviation, and (iii) Coefficient of Quartile Deviation.
See Answer →The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies Y, (Y + 2), (Y - 3) and (Y + 6), respectively. If the arithmetic mean is 4.876, find the value of Y and write the whole series.
See Answer →If (A) = 90, (AB) = 40, N = 150 and (β) = 80 then (αβ) = 30.
See Answer →The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.
See Answer →If each value of X is divided by 2 and of Y is multiplied by 2, then b'YX will be same as b.
See Answer →If X and Y are two independent variables and the variables U = X+ Y and V= X –Y, then the