Exercise 8
Q1.X: Number of patients admitted per week
X ~poisson(7) ; where= 7
The probability mass function (or) of X would be
, for
(a) X: The Number of patients admitted on a particular day
x /0 / 0.3679
1 / 0.3679
2 / 0.1839
3 / 0.0613
….. / …..
Total / 1.0000
X ~poisson(1)
The of X would be
, for
(i) No patients admitted:
= = = 0.3679
(ii) At least 2 patients admitted:
=1[0.3679+ 0.3679] =10.7348= 0.2652
(b) (i)
Hospital is expected to admit 14 patients in 2 weeks.
(ii)
Hospital is expected to admit 28 patients in one month.
x /0 / 0.0498
1 / 0.1494
2 / 0.2240
3 / 0.2240
4 / 0.1680
….. / …..
Total / 1.0000
Q2.X: Number of deaths per year from a cancer
X ~poisson(3) ; where=3
The of X would be
, for
(a) Not more than 2 deaths in a year
=
= 0.0498 + 0.1494 + 0.2240 = 0.4232
(b)At least 2 deaths in a year
= 1[0.0498 + 0.1494] = 10.1992 = 0.8008
(c) exactly 3 deaths in a year
= 0.2240
(d) exactly 4 deaths in 4months
X: Number of deaths in 4 months from cancer
X ~poisson(1)
The of X would be
, for
Exactly 4 Deaths
= 0.0153
Q3.X: Number of cases of breast cancer diagnosed in each year
X ~poisson(6) ; where=6
The of X would be
, for
(a) No new cases in a year
== = 0.0025
(b) Twonew cases in 6 months
X: Number of new cases of cancer in 6months
X ~poisson(3)
== 0.2240
Q8.X: Number of pus cells in the urine of healthy person per one cm3
X ~poisson(2) ; where=2
The of X would be
, for
(a) No pus cells in one cm3
== = 0.1353
(b) Twopus cells in½ cm3
X: Number of pus cells in ½ cm3 of urine
X ~poisson(1)
= = 0.3679
Q4.Let Z ~ N(0,1) ; and
(a) = 0.9131 (b) = 1−
= 1−0.9918=0.0082
(c) = 0.9649 (d)=1−
=1− 0.9965 =0.0035
(e) =-=0.9821− 0.1151 = 0.867
(f) = 0
(g) =−=0.9265 −0.0091=0.9174
Q5.Let Z~ N(0,1) ; and
(a) = 0(b) =1.645(c) = − 1.96(d) =1.96
Q6.Let Z~ N(0,1) ; and
(a) =0.0078 ; From Table:
(b) =0.1290 ; From Table:
(c) =0.9956
1−=0.9956
= 1− 0.9956 = 0.0044
= 0.0044
From Table: −2.62
(d) = 0.1553
−= 0.1553
=+ 0.1553
= 0.8413 + 0.1553 = 0.9966
= 0.9966
From Table: = 0.9966 2.709
Q7.Let Z~ N(0,1) ; and
= 0.0049
1−= 0.0049
=1−0.0049 = 0.9951
= 0.9951
From Table: = 0.9951 = 2.583