HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

From the following data find y at x = 43 and x = 84.

The area A of circle of diameter ‘d’ is given for the following values

Find the approximate values for the areas of circles of diameter 82 and 91 respectively

If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃ = 465

From the following table obtain a polynomial of degree y in x.

Using Lagrange’s interpolation formula find a polynominal which passes through the points (0, –12), (1, 0), (3, 6) and (4, 12)

Find the expected value for the random variable of an unbiased die

Let X be a random variable defining number of students getting A grade. Find the expected value of X from the given table:

The following table is describing about the probability mass function of the random variable X

Find the standard deviation of x.

Let X be a continuous random variable with probability density function
`"f"_x(x) = {{:(2x",", 0 ≤ x ≤ 1),(0",",  "otherwise"):}`
Find the expected value of X

Let X be a continuous random variable with probability density function
f(x) = `{{:(3/x^4",",  x ≥ 1),(0",",  "otherwise"):}`
Find the mean and variance of X

In investment, a man can make a profit of ₹ 5,000 with a probability of 0.62 or a loss of ₹ 8,000 with a probability of 0.38. Find the expected gain

What are the properties of Mathematical expectation?

What do you understand by Mathematical expectation?

How do you defi ne variance in terms of Mathematical expectation?

Define Mathematical expectation in terms of discrete random variable

State the definition of Mathematical expectation using continuous random variable

In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?

The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
f(x) = `{{:(1/30 "e"^(- x/30)",",  "for"  x > 0),(0",",  "for"  x ≤ 0):}`
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point

A person tosses a coin and is to receive ₹ 4 for a head and is to pay ₹ 2 for a tail. Find the expectation and variance of his gains

Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5?