ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 128 - 134 of 164

To solve the equation f (x) = 0, using Lagrange՚s inverse interpolation method

We known that the L. H. S. is an incomplete gamma function and R. H. S. is a cumulative density function of Poisson distribution.

The incomplete gamma function is

Then

provided that r is an integer. Thus recall that Γ (r) = (r − 1) ! for r integer.

Rewriting this expression we arrive at the desired expression

Let M₁ and M₂ is the median temperature of the patients. The hypothesis for test is

Fir this first find the difference of median

Also find the difference of temperature of before and after

d_i 2.1 4.9 2.0 1.0 3.9 3.4 1.7 4.6 2.4 3.7

Then find the sign of difference between d_i and d₀ .

-+ -- ++ -+ -+

The number of positive sign is r = 5 and negative sign i…

We have to prove that

By definition of Kurtosis

Let x₁ , x₂ , … , x_n are n observations in a set have frequency f₁ , f_2, … , f_n and the mean of observation is , then

Assume

which is always true because this a variance which is always positive

So, ‎

Here, you would know the standard deviation of a population but not know the mean of that population. So, you want to estimate the mean μ to within a given margin of error in a given confidence interval. The required sample size is

Margin of error E = 0.5,

1-α = 0.95 ⇾ α = 0.05

σ = 1 and z_α/2 = 1.96

If x₁ , x₂ , … , x_n are the values having weights w₁ , w₂ , … , w_n respectively, the weight mean is

Here X is first ‘n’ natural numbers that is 1,2, 3, … , n

his is not exponential equation, it is a straight line y = a + bx

The normal equations is

Using the table , putting these values in normal equations. We get

Solving these two equations, we get the value of a and b

So, required line is y = 2.188 + 6.677x