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Math
Solve the system of equations
2 (x1) + 3 (x2) +4 (x3) + (x4) =3
(x1) + 2 (x2) + (x4) =2
2 (x1) + 3 (x2) + (x3) - (x4) =1
(x1) - 2 (x2) - (x3) + 4 (x4)=5
using Gauss elimination method with pivoting.
2 (x1) + 3 (x2) +4 (x3) + (x4) =3
(x1) + 2 (x2) + (x4) =2
2 (x1) + 3 (x2) + (x3) - (x4) =1
(x1) - 2 (x2) - (x3) + 4 (x4)=5
using Gauss elimination method with pivoting.
Math
Using Xo = 0 find an approximation to one of the zeros of x^3 − 4x +1 = 0 by using Birge Vieta Method. Perform two iterations
Math
Find an approximate value of the positive real root of xe^x =1 using graphical method. Use
this value to find the positive real root of xe^x =1 correct to three decimal places by fixed
point iteration method.
this value to find the positive real root of xe^x =1 correct to three decimal places by fixed
point iteration method.
Math
Using Maclaurin’s expansion for sin x , find the approximate value of sin (π/4) with the error
bound 10^(−5) .
bound 10^(−5) .
Math
Find an appropriate root of x^3 + 2x^2 − 5 = 0 in [1,2 ] with 10^(−5) accuracy by
i) Newton Raphson Method
ii) Secant Method
What conclusions can you draw from here about the two methods?
i) Newton Raphson Method
ii) Secant Method
What conclusions can you draw from here about the two methods?
Evaluate the integral +
/ 2
0
2 cos
1
p
dx
x
.
/ 2
0
2 cos
1
p
dx
x
.
a) A sample of size 36 is picked at random from a population of adult males. If the standard
deviation of the distribution of their heights is known to be 3 cms, find the standard error of
the mean if
i) the population consists of 1000 males.
ii) the population is extremely large. (3)
b) Suppose the gene ‘A’ stands for tall and gene ‘a’ stands for short, and ‘A’ is dominant over
‘a’. Suppose the parents are of genotype aa and Aa.
i) In a family like this what is the probability of having a short child?
ii) In a family like this if there are four children, what is the probability that two children
are tall and two children are short?
iii) If you survey a large number of such families having four children, what is the average
number of tall children to be expected in a family?
iv) If you survey 256 families of this type, each having four children, how many families
are expected to have all tall children?
deviation of the distribution of their heights is known to be 3 cms, find the standard error of
the mean if
i) the population consists of 1000 males.
ii) the population is extremely large. (3)
b) Suppose the gene ‘A’ stands for tall and gene ‘a’ stands for short, and ‘A’ is dominant over
‘a’. Suppose the parents are of genotype aa and Aa.
i) In a family like this what is the probability of having a short child?
ii) In a family like this if there are four children, what is the probability that two children
are tall and two children are short?
iii) If you survey a large number of such families having four children, what is the average
number of tall children to be expected in a family?
iv) If you survey 256 families of this type, each having four children, how many families
are expected to have all tall children?
a) The genetic features of a group of adult mice are such that the probability of an offspring
being albino is 0.2. If 50 offsprings are born to a group of such mice, find the probability that
15 or more of them are albinos. (4)
b) The urinary secretion rate (mg./24 hours) of patients suffering from disease A is normally
distributed with mean 5 variance 1, while the corresponding rate for disease B is normally
distributed with mean 7 variance 4. A patient is classified as suffering from disease A and
disease B if his rate is more than 5.5 and up to 5.5 respectively. What is the probability of
misclassification if disease A is twice as common as disease B?
being albino is 0.2. If 50 offsprings are born to a group of such mice, find the probability that
15 or more of them are albinos. (4)
b) The urinary secretion rate (mg./24 hours) of patients suffering from disease A is normally
distributed with mean 5 variance 1, while the corresponding rate for disease B is normally
distributed with mean 7 variance 4. A patient is classified as suffering from disease A and
disease B if his rate is more than 5.5 and up to 5.5 respectively. What is the probability of
misclassification if disease A is twice as common as disease B?
A bag contains 8 white balls and 4 red balls. One ball is drawn from the bag and it is
replaced after noting its colour. In the second draw again one ball is drawn and its color is
noted. Find the probability that both the balls drawn are of different colours?
replaced after noting its colour. In the second draw again one ball is drawn and its color is
noted. Find the probability that both the balls drawn are of different colours?
Math
The thickness of the ice on a lake for one week is modelled by the function:a) T(d)=-0.1d^3+1.2d^2-4.4d+14.8
where T is the thickness in cm and d is the number of days after December 31st. The graph of the function is provided below.
a) Determine the average rate of change in the thickness of the ice over 7 days.
b) When do you think the warmest day occurred during the week? Justify your answer.
c) Estimate the instantaneous rate of change at the point you chose in b).
d) Why is this called the estimated instantaneous rate of change?
e) Were your answers to the average rate of change the same as the estimated instantaneous rate of change? Explain why or why not.
where T is the thickness in cm and d is the number of days after December 31st. The graph of the function is provided below.
a) Determine the average rate of change in the thickness of the ice over 7 days.
b) When do you think the warmest day occurred during the week? Justify your answer.
c) Estimate the instantaneous rate of change at the point you chose in b).
d) Why is this called the estimated instantaneous rate of change?
e) Were your answers to the average rate of change the same as the estimated instantaneous rate of change? Explain why or why not.
