STA301 Midterm Solved Subjective 2012

STA301- Statistics and Probability · Solved Subjective · From Midterm Papers · DEC 19,2012 · PSMD01

The numbers of airplane accidents in a year are 1, 2, 3, 4 with corresponding probabilities 1/6, 2/6, 2/6 and 1/6. What is the variance of annual accidents?

Solution:-

X P PX X2 PX2

Total PX  PX 

PX E X PX E X

VAR(X) = E(X)2 - EX2 “If P (A|B) = P (B|A) then P (A) = P (B)”.

Indicate whether the above statement is true or false? Also give reason. Solution:-

Yes this statement is true, because P A B P A B and P B

P A B P B A therfore P A Therefore there is difference just in denominator If the Values of P (A|B) = P (B|A re same then the denominator should also be same

Why we use coefficient of variation?

Answer: (Page 93) We calculate variation if we have to compare different data with the same variable but with very different arithmetic means.

Q1. find the missing value in the formula ? ( Marks: 2 )

Answer: (Page 159) P (B) is missing.

Q2. what is Coefficient of Correlation? ( Marks: 2 )

Answer: (Page 128) A numerical measure of the strength of the linear relationship between two random variables X and Y is known as Pearson’s Product-Moment Coefficient of Correlation.

Q3. why the mean of the probability distribution of a random variable X is technically called the EXPECTED VALUE of the random variable X ? ( Marks: 3 )

Answer: (Page 170) Because we expect the mean from of the random variable from the data.

Q4. For the give data

Means = 3.8,

Median = 2.3 and

Standard Deviation = 1.3,

Now Find the Pearson's Coefficient of skweness ? ( Marks: 2 )

3. 8
4. 3
5. 154
6. 3 mean median S D

It is positively skewed

Q5. Compute the mean deviation from mean for the following data (where Mean = = 40.4) ( Marks: 5 )

Answer: X F X X 40.4 X  f X X

10.4 41.6 33.4 233.8 0.4 4.4 4.6 36.8 9.6 f  364.4 f X X

M.D = 364.4 10.41 f X X

n

Q: A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 2/7 and probability of wife’s selection is 3/5. ( Marks: 5 ) What is the probability that

(a)Both of them will select?

(b)Only one of them is selected · (c)None of them is selected · X · F