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- Suppose a person throws a die. If he gets a 5 or 6, he tosses a coin three times and notes the number of heads. If he gets 1, 2, 3 or 4, tosses a coin once and notes whether a head or tail is obtained. If he obtained exactly one head; what is the probability that he threw 5 or 6 with the die.
The solution to this problem involves Bayes’ theorem, which states that P(A|B) = P(B|A) * P(A) / P(B), where P(A|B) is the probability of event A given event B is true, P(B|A) is the probability of event B given event A is true, P(A) is the probability of event A, and P(B) is the probability of event B.
We want to find the probability that the die
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- A random variable has the following probability distribution
Find (i) the value of ‘’
Solution: Since it is a probability distribution, so, sum of all probabilities must be 1
Since, “a” is a probability, so, it cannot be negative
A = 0.1
When 1.5<x<4.5 =2a+3a
=1/2 or 0.5
When x>2 =P(X=3)+ P(X=4)+ P(X=5)+ P(X=6)+ P(X=7)
= 2a+3a+ a2+2a2+7a2
- The daily earning of a vendor for a period of 43 days are given below
|Daily earning (Rs.)||118-126||127-135||136-144||145-153||154-162||163-171||172-180|
|No. of days||3||8||9||12||5||4||2|
Calculate Standard Deviation and coefficient of variation.
|Daily earnings||f||x||fx||(x-x̄)||F(x- x̄)||f(x- x̄)2|
- The probability that a bomb dropped from a plane will strike the target is 1/5. If 6 bombs are dropped, find the probability that-
- Exactly two will strike the target.
- Atleast two will strike the target.
To answer this question, we’ll need to use the binomial probability formula, which is as follows:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where: P(X=k) is the probability of k successes in n trials, C(n, k) is the number of combinations of n items taken k at a time (also known as “n choose k”), p is the probability of success on a given trial, and (1-p
- Compute the regression equation of Y on X and regression equation of X on Y on the basis of the following information
The correlation coefficient between X and Y is 0.50.
Also estimate the value of Y for X = 48, using the appropriate regression equation.
- The following data relate to the prices and quantities of 4 commodities in the years 1982 and 1983. Construct the following index numbers of price for the year 1983 by using 1982 as base year.
- Laspeyre’s Index
- Paasche’s Index
iii. Fisher’s Index