Statistics Questions

Fisher's index number is the:

The index number for the price of diesel in $2015$ was $125$ and in $2016$ it was $140$, with $2011$ as the base year. What is the percent increase in the price of diesel from $2015$ to $2016$?

Calculate the index number using the simple average of price relative method for the data below, taking 2010 as the base year:ItemPrice in 2010Price in 2015A100140B80120C160200D220385E112112

A medicine is known to be $75\%$ effective. If the medicine is given to 5 patients, what is the probability that at least one patient is cured?

Given that $x\sim B(n=10,p)$, if the expectation $E(x)=8$, find the value of $p$.

Consider the following statements regarding index numbers:(i) Simple average of price relative is a weighted index numbering method.(ii) The index number for the base year is always 100.(iii) If the price index is 25, then the prices have increased by 25%.(iv) If the price index is 75, then the prices have decreased by 25%.Which of the statements are correct?

A time-series data is represented by the line $y=a+bx$. If the middle time period is taken as origin ($\sum x=0$), and it is found that $\sum xy=6$ and $\sum x^2=5$, what is the value of '$b$ '?

In the following table, $x$ is the discrete random variable and $p(x)$ is the probability density function. The standard deviation of $x$ is:| $x$ | $1$ | $2$ | $3$ | $4$ ||---|---|---|---|---|| $p(x)$ | $0.2$ | $0.4$ | $0.3$ | $0.1$ |

The variance ${\sigma }^2$ of a random variable $X$ is given by:

Which of the following is correct regarding the analysis of four components of time series analysis?

Using the base year 1985, the index number calculated by the simple aggregate method for four items (A, B, C, D) is $125$. Given:Prices in 1985: $75,85,\alpha ,100$ Prices in 1986: $90,115,75,\beta$ Find the value of $(4\beta -5\alpha )$.

If $X$ and $Y$ are random variables such that $E(X)=10$, $V(X)=25$ and $E(Y)=0$, $V(Y)=1$, the values of $a,b$ such that $Y=aX-b$ will be:

In the same five-year plan (Total $₹36,000$ crore), how much money is allocated to Education if its angle is $30^{\circ }$?

In a five-year plan with a total allocation of $₹36,000$ crore, the angle for Employment is $120^{\circ }$. Which head is allocated maximum funds if the angles are Agriculture ($90^{\circ }$), Industry ($45^{\circ }$), Education ($30^{\circ }$), and Miscellaneous ($75^{\circ }$)?

A study investigates if the average sunlight in February was greater than the annual average of $5$ units/m${}^2$. What is the null hypothesis ($H_0$) for this problem?

How much excess money is allocated to Miscellaneous (Angle: $75^{\circ }$) over Education (Angle: $30^{\circ }$)?

In the same plan, how much money is allocated to both Agriculture (Angle: $90^{\circ }$) and Employment (Angle: $120^{\circ }$)?

Which of the following methods is used to analyze the simple trend of time series data?