Statistics and Probability Answers

For the random variable X with the following probability density function
f (x) ={2e^(-2x); 0 is greater than equal to x and 0; 0 is smaller than x
find
i) ) P (| X − μ | >1
ii) Use Chebyshev’s inequality to obtain an upper bound on P[| X − μ | >1] and
compare with the result in (i).

Which of the following statements are true or false? Give reasons for your answers. iv) If correlation coefficient between x and y is 0.62., then correlation coefficient between u and v will by 0.62, where U=5+6xand V =7-3y

Which of the following statements are true or false? Give reasons for your answers. By Chebyschev’s inequality, P{mode of x- my greater than equal to 2 sigma} smaller than equal to 0.2

Which of the following statements are true or false? Give reasons for your answers. i) If X has the distribution N(9,10)and if Y=5x-3, then Y has distribution N(84,53)

true or false? Give reason
If correlation coefficient between x and y is 0.62 , then correlation coefficient
between u and v will be 0.62 , where u = 5 + 6x and v = 7 − 3y .

true or false? Give reason
If X has the distribution N(10, 9) and if Y = 5X − 3, then Y has distribution
N(53,84) .

Find all the basic solutions of the following system of equations:

x1 + 2x2 + x3 = 14

3x1 + x2 + x3 = 12

Which of these solutions are basic feasible solutions?

The construction of a building may be delayed by a strike. Suppose that the
probability that there will be a strike is 0.70, the probability that the construction
will be completed on time if there is no strike is 0.90 and the probability that the
building will be completed on time if there is a strike is 0.40, what is the
probability that the construction will be completed on time.

Compute the appropriate regression equation for the following data:
X Y
2 18
4 12
5 10
6 8
8 7
11 5

Where X is the independent variable and Y is the dependent variable.
Also find the correlation coefficient between X and Y and infer about the
relationship between X and Y.

Consider a random sample (WOR) of two industries from a population of 5
industries having yearly turnover as follows:

Industry Turnover (in lakhs)
1 2000
2 2400
3 1800
4 3000
5 2600

Enumerate all possible samples (WOR) of size two and show that the sample
mean gives an unbiased estimate of population mean