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EQT 272 Probability and Statistics
Semester 2
2015/2016
Tutorial 2
1. Determine whether the following random variables are discrete or continuous.
i) The number of eggs that a hen lays in a day.
ii) The amount of milk a cow produces in one day.
iii) The cost of making a randomly selected movie.
iv) The number of goals scored by a randomly selected football player in a soccer game.
2. Determine the value of c so that the following function is a probability density function for a
discrete random variable.
 x2 5 
f  x   c    for x  0,1, 2,3, 4,5
 2 2
3. A factory manufactures DVDs. Batches of DVDs are randomly selected. The number of defects X
for each batch is observed and the following distribution is obtained.
X
0
1
2
3
4
5
P(X=x)
0.502
0.365
0.098
0.023
0.011
0.001
i)
Verify whether the distribution is a probability distribution
ii) Find P  X  2 
iii) Find P  0  X  4
iv) Find the E  X  , Var  X  and standard deviation X.
4. A random variable X has the following distribution:
X
1
2
P(X=x)
3b
2b
i)
Find the value of b.
ii) Find P 1  X  4
iii) Find Var  X 
5. Let the following function of a random variable Y be
, 0  y 1
 y

f  y   2  y , 1  y  2
 0
, otherwise

i) Check whether the function is a probability density function
ii) Find the cumulative distribution function.
iii) Find P  0.5  X  0.9 
iv) Find P  0.75  X  1.5
v) Calculate E  X  and Var  X 
3
0.4
4
0.1
EQT 272 Probability and Statistics
6. If a random variable X has probability density function
2

0 x5
 B  x  4 x  5 ,
f  y  
0
, x  0 or x  5


Calculate the value of B.
7. Suppose X is a random variable with the following distribution function.
0
,
x0


3
 3  2 x 
F  y  
 4x   , 0  x  8
3 
 256 

1
,
x>8

i)
Find P  1  X  2
ii) Find f  x 
Semester 2
2015/2016