Question
Explain the importance of time series.
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Answer
self-study
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Among the various vehicle owners visiting a petrol pump, $80\%$ vehicle owners visit to fill petrol in their vehicle and $60\%$ vehicle owners visit to fill air in their vehicles. $50 \%$ vehicle owners visit to fill air and petrol in their vehicle. Find the probability for the following events:
$(1)$ If a vehicle owner has come to fill petrol in his vehicle, then that vehicle owner will fill air in his vehicle.
$(2)$ If a vehicle owner has come to fill air in his vehicle, then that vehicle owner will fill petrol in his vehicle.
→$(1)$ If a vehicle owner has come to fill petrol in his vehicle, then that vehicle owner will fill air in his vehicle.
$(2)$ If a vehicle owner has come to fill air in his vehicle, then that vehicle owner will fill petrol in his vehicle.
Discuss the merits and limitations of the method of moving averages.
Three events $A, B$ and $C$ in a sample space are mutually exclusive and exhaustive. If $4P (A) = 5P (B) = 3P (C),$ then find $P (A \cup C)$ and $P(B \cup C).$
→Obtain the derivatives of the following function with the help of definition :
→$f(x)=\frac{2}{3 x-4}, \quad x \neq \frac{4}{3}$
The following information is given for ten firms running business of clothes in a city regarding their average annual profit $($in lakh $₹)$ and average annual administrative cost $($in lakh $₹) :$
→The following informatino is given for ten firms running business of clothes in a city regarding their aerage annual profit $($in lakh $i‘)$ and average annual administrative cost $($in lakh $₹) :$
Obtain the regression line of $Y$ on $X.$
OR If the regression line is $\hat{y}=\frac{x}{2}+5$ and $S_y: S_x=5: 8$.
Find the co-efficient of determination.
→| Particular | Profit (in lakh ₹) X |
Administrative Cost (in lakh ₹) Y |
| Mean | $60$ | $25$ |
| Standard Deviation | $6$ | $3$ |
| Covariance ; $10.4$ | ||
OR If the regression line is $\hat{y}=\frac{x}{2}+5$ and $S_y: S_x=5: 8$.
Find the co-efficient of determination.
The regression line of $Y$ on $X$ is $6 x+8 y-64=0$ and the variance of $Y$ is $4$ times of the variance of $X$. If the value of $X$ changes by $4$ units, what will be the effect on the value of $Y\ ?$ Also find $R^2$ and interpret it.
→Find the probability of having 5 Tuesdays in the month of August of any year.
If $P(M)=P(F)=\frac{1}{2}, P(A \mid M)=\frac{1}{10}$ and $P(A \mid F)=\frac{1}{2}$ for events $A, M$ and $F,$ then find $P(A \cap M)$ and $P(A \cap F)$.
→State properties of binomial distribution.