HW Specic Instructions 1. For the probability problems include the appropriate p
ID: 3175214 • Letter: H
Question
HW Specic Instructions
1. For the probability problems include the appropriate probability statements [Ex. P(A|B), P(X = 15), P(3 X < 5), etc.]
2. Use appropriate notation.
3. ALL probabilities MUST be reported in 4 decimal digits.
4. When using the calculator to compute probabilities/percentiles, provide the calculator function and its arguments.
Suppose the variable Q has the following distribution:
q
1
4
7
10
P(Q= q)
0.1
0.4
0.2
C
(a) Compute the value of C.
(b) Compute the expected value of Q.
(c) Compute the variance of Q.
(d) Compute the standard deviation of Q.
(e) Suppose that M(Q) = 100 4 Q.
i. Compute the expected value of M(Q).
ii. Compute the variance of M(Q).
q
1
4
7
10
P(Q= q)
0.1
0.4
0.2
C
Explanation / Answer
a) for it top be valid pdf sum of all probabilty should equal to 1
0.1+0.4+0.2+C=1
C=0.3
b)expected value =E(Q) =1*0.1+4*0.4+7*0.2+10*0.3=6.1
c)E(Q2) =12*0.1+42*0.4+72*0.2+102*0.3 =46.3
hence variance =Var(Q) =(E(Q2)-(E(Q))2 =9.09
d)Std deviation =SD(Q) =(Var(Q))1/2 =3.015
e)(i) E(M)=100-4*E(Q)) =100-4*6.1=75.6
(ii) Var(M)=(4*SD(Q))2 =(4*3.015)2 =145.44
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