SOLUTION: Question 2 A.The table below shows the probability distribution for a discrete random variable X. X 0 1 2 4 5 P(X=x) 0.15 0.20 n 0.30 0.10 Table 2. i.State the value of n

Algebra ->  Probability-and-statistics -> SOLUTION: Question 2 A.The table below shows the probability distribution for a discrete random variable X. X 0 1 2 4 5 P(X=x) 0.15 0.20 n 0.30 0.10 Table 2. i.State the value of n       Log On


   

Question 1203397: Question 2
A.The table below shows the probability distribution for a discrete random variable X.
X 0 1 2 4 5
P(X=x) 0.15 0.20 n 0.30 0.10
Table 2.
i.State the value of n (1 mark)
ii.Calculate the expectation value, E(X) (4 marks)
iii.Calculate the variance, Var(X) (5 marks)
B.A random variable X follows a Normal probability distribution and has a mean value of 25 and a variance of 9. Calculate:
i.P(X < 21) (3 marks)
ii.P(X > 26) (3 marks)
iii.P( 23 < X < 28) (4 marks)
Answer by mntnvisions(1) About Me  (Show Source):
You can put this solution on YOUR website!
The total probability must be 1.0
Add the probabilities and solve for n.
P=1=+0.15+%2B0.20+%2Bn+%2B0.30%2B+0.10
n=1-0.75=0.25
n=0.25
Mean or average value, use n=0.25 value.
E%28x%29=sum+%28xP%28x%29%29=0%2A0.15%2B++1%2A0.2%2B++2%2A0.25%2B++4%2A0.3%2B++5%2A0.1+=2.4

Variance.


B.A random variable X follows a Normal probability distribution and has a mean value of m=25 and a variance of Var=9. Calculate:
Standard deviation = +s=sqrt%28Var%29=sqrt%289%29=3.
i.P(X < 21):
z=%28X-m%29%2Fs=%2821-25%29%2F3=-4%2F3
P%28Z+%3C+-1.333%29=0.0912
ii.P(X > 26)
z=%28X-m%29%2Fs=%2826-25%29%2F3=1%2F3
P%28Z+%3E+0.333%29=1-P%28Z+%3C+0.333%29=1-0.631=0.369

iii.P( 23 < X < 28):

a=%28X-m%29%2Fs=%2823-25%29%2F3=-2%2F3
b=%2828-25%29%2F3=1
P%28-0.667+%3CZ+%3C+1%29=P%28Z+%3C+1%29-P%28Z+%3C+-0.667%29=0.841-0.252=0.589