## User: tanya.tanyabarnwal

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#### Academic profile

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Answer:
A: Chapter 3 .

... **Solution:**
(i) p=10%=0.1
q=1-p=0.9
n=5
$P(X=Y)=^{n}C_{r}p^{r}q^{n-r}$
For at the most two are defective r=0, 1, 2
$P(X=0 \ or \ 1 \ or \ 2)=^{5}C_{0}(0.1)^{0}(0.9)^{5}+^{5}C_{1}(0.1)^{1}(0.9)^{4}+^{5}C_{2}(0.1)^{2}(0.9)^{3}$
$P(X=0 \ or \ 1 \ or \ 2)=0.59049+0.32805+0.0729=0.99144$
(ii) ...

written 5 weeks ago by
tanya.tanyabarnwal •

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Chapter 2. Show that the matrix $A$ satisfies Cayley-Hamilton Theorem and hence find $A^{-1}$, where

... $A=\begin{bmatrix} 1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1 \end{bmatrix}$ ...

written 5 weeks ago by
tanya.tanyabarnwal •

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... Use the dual simplex method to save the following LPP:
Minimize, $z=2x_{1}+x_{2}$
subject to,
$3x_{1}+x_{2} \ge 3$
$4x_{1}+3x_{2} \ge 6$
$x_{1}+2x_{2} \le 3$
$x_{1}, \ x_{2} \ge 0$ ...

written 5 weeks ago by
tanya.tanyabarnwal •

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... Justify if there is any relationship between sex and color for the following data:
| Color | Male | Female |
|:-----:|:----:|:------:|
| Red | 10 | 40 |
| White | 70 | 30 |
| Green | 30 | 20 | ...

written 5 weeks ago by
tanya.tanyabarnwal •

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... Check whether the following matrix is derogatory or non-derogatory.
$A=\begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix}$ ...

written 5 weeks ago by
tanya.tanyabarnwal •

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... (i) If 10% of the rivets produced by a machine are defective, find the probability that out of 5 randomly chosen rivets at the most two will be defective.
(ii) If x denotes the outcome, when a fair dice is tossed, find the M.G.F. of x and hence find the mean and variance of x. ...

written 5 weeks ago by
tanya.tanyabarnwal •

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Answer:
A: Chapter 1 .

... **Solution:**
Consider, $\int_{0}^{2\pi}\cfrac{\cos{2 \theta}}{5+4 \cos {\theta}} d\theta$
Put $z=e^{j \theta}$ -----------(1)
$dz=j e^{j \theta} d\theta$
$d\theta=\cfrac{dz}{jz}$ ---------------(2)
$\cos {\theta} = \cfrac{e^{j \theta} + e^{-j \theta}}{2} =\cfrac{z+z^{-1}}{2}=\cfrac{z+\cfrac{1} ...

written 5 weeks ago by
tanya.tanyabarnwal •

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... Using the residue theorem, Evaluate $\int_{0}^{2\pi}\cfrac{\cos{2 \theta}}{5+4 \cos {\theta}} d\theta$. ...

written 5 weeks ago by
tanya.tanyabarnwal •

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Answer:
A: Chapter 4 .

... **Solution:**
$\bar{X}=9.3, \ \mu=8.9, \ s=1.6, \ n=50$
(i) Null Hypothesis $(H_{o}): \ \mu_{1}=\mu_{2}$
Alternate Hypothesis $(H_{a}): \ \mu_{1} \ne \mu_{2}$
(ii) Test statistic
$Z=\cfrac{\bar{X}- \mu}{s/ \sqrt{n}}= \cfrac{9.3-8.9}{1.6 / \sqrt{50} }=1.7678$
(iii) Level of significance at 5%, ...

written 5 weeks ago by
tanya.tanyabarnwal •

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... An ambulance service claims that it takes on an average 8.9 minutes to reach the destination in emergency calls. To check this the licensing agency has then timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. Is this acceptable at 5% LOS? ...

written 5 weeks ago by
tanya.tanyabarnwal •

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