1 Marks Each

Question 11 Mark

Find $\frac{d y}{d x}$ if $y=6 x^3+\frac{7}{2} x^2+\frac{6}{5} x-8$

Answer

$y=6 x^3+\frac{7}{2} x^2+\frac{6}{5} x-8$
$\therefore \frac{d y}{d x}=18 x^2+7 x+\frac{6}{5}$

Question 21 Mark

Define the $\delta$ neighbourhood of $a$.

Answer

If $a \in R$ and $\delta$ is non-negative real number then the open interval $(a-\delta, a+\delta)$ is called $\delta$ neighbourhood of $a$.

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Question 31 Mark

What percentage of area is covered under the normal curve within the range $\mu-2 \sigma$ to $\mu+2 \sigma$ ?

Answer

$94.45 \%$ of area is covered under the normal curve within the range $\mu-2 \sigma$ to $\mu+2 \sigma$

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Question 41 Mark

Give the values of the constants used in probability density function of normal variable.

Answer

$\pi=3.1416$
$e=2.7183$

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Question 51 Mark

Define Bernoulli trials.

Answer

Suppose dichotomous random experiment has two outcomes, success $(S)$ and failure $(F).$ If this experiment is repeated $n$ time under identical conditions and the probability $p(0< p<1 )$ of getting a success at each trial is constant then such trials are called Bernoulli Trials.

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Question 61 Mark

State the formula for the probability of occurrence of at least one event out of three events $A , B$ and $C$.

Answer

$P ( A \cup B \cup C )= P ( A )+ P ( B )+ P ( C )$$- P ( A \cap B )- P ( A \cap C )- P ( B \cap$C) $+P(A \cap B \cap C)$

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Question 71 Mark

What is a time-series?

Answer

The data collected and arranged according to the time is called timeseries. OR A time series is a set of observations taken at specified time periods.

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Question 81 Mark

Give the name of a method to obtain the best fitted regression line.

Answer

Method of least square is used to obtain the best fitted regression line.

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Question 91 Mark

What is the main limitation of scatter diagram method to find correlation coefficient?

Answer

The main limitation of scatter diagram is that it gives only nature of correlation and some idea about the strength of correlation, but it does not give exact degree of relationship between two variables.

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Question 101 Mark

Name the important basic tests of index numbers.

Answer

The important basic tests of index number are : $(1)$ Time reversal test $(2)$ Factor reversal test.

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Statistics 1 Marks Each

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