Page 187 - Engineering Mathematics Workbook_Final

Probability & Statistics

142. Rock bolts have length L = (150 + X) (a) 0.2 (b) 0.4
cm, where X is a random variable
with PDF. (c) 0.5 (d) 0.6

 1 Joint Distribution

−
2
x

f ( ) x =  4 (1 3x ) if −   2 146. The joint probability mass function of

 0, Otherwise (X, Y) is given below.

If 95% of the bolt lengths (L) lie in x→ 1 2 3
the interval 150 – C cm to 150 + C y↓ 3k 6k 9k
0
cm, the value of C is _______. 1 5k 8k 11k
2 7k 10k 13k
143. A random variable X has probability
density function as given below: Find (i) k

P
(ii) (x  ) 1

f ( ) x = + for 0 x  1
a bx

= 0 Otherwise (iii) (1 x  3, y  ) 1

P
2
E
If expected value ( ) x = , then 147. Two random variables X and Y are
3 distributed according to
P x  0.5  is
r

 x + 0   1,0  y 

144. A random variable X has the f ( , x y =  y x 1
)
following probability function. , x y  0 otherwise


X 0 1 2 3 4 5 6
P(X) K 3 5 7 9 11 13 The probability
K K K K K K
Find   1     1  
(i) p x  2    (ii) p y  2   



P
(i) K (ii) (3 x  ) 6    
 1 1 
(iii) Mean (iv) Variance (iii) p x    / y     
 2 2 
145. In a lottery there are 200 prizes of Rs.

5, 20 prizes of Rs. 25 and 5 prizes of (iv) ( p x + y  ) 1
Rs. 100. Assuming that 10,000 prizes
tickets are to be issued and sold.
What is the fair price to pay for the
ticket? (or if some one purchases a
lottery ticket his expectations is)

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