Statistics Quiz (I)
1) For a forward difference table the points $$(x_0,y_0),(x_1,y_1),(x_2,y_2),dots$$ with $$h=x_1-x_0=x_2-x_1=dots$$ so on, and for the function $$y=x^n,$$ say, which of the following statements is true?
A) $$frac{Delta^2y_0}{h^2}=12$$
B) $$frac{dy}{dx}=3x^2$$
C) $$frac{d^2y}{dx^2}=6x|_2=12$$
D) $$frac{Delta^2y_0}{h^2}=frac{d^2y}{dx^2}|_{x=x_1}$$
2) “If $$f(x)$$ is continuous in $$(a,b),$$ then for any $$x$$ in that interval, we shall have a polynomial $$P(x)$$ such that
$$P(x)-epsilon<f(x)<P(x)+epsilon, epsilon >0.$$ ”
Which mathematician is this theorem due to?
A) Simpson
B) Weistrass
C) Riemann
D) Newton
3) In theorizing Simpson’s $$frac{1}{3}rd$$ rule of integration, it was presumed that the integrand has to be approximated by a second degree polynomial. If this condition is not satisfied, we usually take small values of the length of the interval, h. However to integrate
$$int_0 ^{10}x^3dx=2500,$$
A) two intervals will be sufficient.
B) more than two intervals will be needed.
4) Fpr the sample points $$x_1,x_2,dots ,x_n,$$ $$overline{x}=frac{sum_ix_i}{n}$$ is a
A) Least Square Estimation of $$mu.$$
B) Maximum Likelihood Estimation of $$mu.$$
C) Maximum Chi-square Estimation of $$mu.$$
D) None of the above.
5) For the linear equation
$$y_i=a+bx_i+epsilon_i,$$
say, $$hat{y_i}=hat{a}+hat{b}x_i.$$
Then $$frac{sum_i(y_i-hat{y_i})^2}{sum_i(y_i-overline{y})^2}$$ is
A) Co-efficient of determination.
B) Co-efficient of non-determination.
C) Co-efficient of variation.
D) Co-efficient of correlation.
6) For a Bernoulli random variable, if $$p$$ is the probability of success and $$q$$ is the probability of failure, then the $$max(p,q)$$ is
A) 1
B) 0
C) $$frac{1}{2}$$
D) $$frac{1}{4}$$
7) If $$X$$ is a binomial variate with mean $$np$$ and variance $$np(1-p),$$ then which of the following statements will be sufficient for $$X$$ to follow the Poisson Law:
A) $$prightarrow 0, nrightarrow infty.$$
B) $$prightarrow 0, nrightarrow infty, np$$ finite.
C) $$prightarrow 0, np$$ finite.
D) $$nrightarrow infty, np$$ finite.
8) In measuring trend by the method of moving average, the no, of terms to be considered for averaging is decided by
A) the length of the shortest circle.
B) the no of cycles.
C) the length of cycles.
D) none of the above.
9) If $$x_1,x_2,dots ,x_n$$ are $$n$$ random observations, then
$$T_n=sum_{i=1} ^nx_i$$ is
A) a random variable, but not a stochastic process.
B) a stochastic process.
C) neither a random variable nor a stochastic process.
D) a stochastic process, but not a random variable.
10) The Weiner stochastic process with constant time is known in the theory of statistics as the
A) Binomial Distribution.
B) Poisson Distribution.
C) Normal Distribution.
D) Hyper Geometric Distribution.
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Answers:
1) D , 2) B , 3) A , 4) A , 5) B , 6) D , 7) D , 8) A, 9) B , 10) C.
Dhruba Das
Research Scholar, Department of Statistics,
Gauhati Uiniversity.