STA301 Final Term Solved Papers Set 3

Final-term EXAMINATION · SEMESTER Fall 2004 · STA-301 Statistics and probability(Paper-1)

2. Do not ask ay questions about the contents of this examination from anyone.
3. You are allowed to use the calculator & Statistical tables in order to solve the questions.
4. For your convenience we are providing you the following symbols,

 ,∩, X ‘ t , t (v) , 1 ,  2 , , 1, 2 , 3 ,  , 2 , 3 , 2 , 4 ,  x,  y,  xy,  x2 ,  +

2(v) y 2 , Name. Questions

Marks

Questions

Marks Total

Q1. Marks:1

If mean=median=mode then curve is symmetric. o True o False

Q2. Marks:1

Distribution Function is also called the step function. o True o False

Q3. Marks:1

In the case of sampling with replacement as well as in the case of sampling without replacement, we have:

o True o False

Q4. Marks:1

The rejection region is also called the critical region. o True o False

Q5. Marks:4

Describe the continuous and discrete random variable with example.

Continuous Random Variable:

A random variable is called continuous if the set of value is an entire interval on the number line i.e., the sample space S is continuous. The outcomes of an experiment are represented by the point on the line.

Discrete Random Variable:

A random variable is called discrete if the set of values it taken is a collection of isolated points on a real line i.e., the sample space S is a discrete sample space. The outcomes of an experiment is noted.

Q6. Marks:4

Define and describe the Least Significance Difference (LSD).

When the null hypothesis of equal means is rejected by F-Test after the ANOVA we can test the significance of difference between means of treatments by using the ordinary two samples t-Test on every pair at significance level α. The smallest difference is called the least significance difference(LSD) and is given by: 2(

v MSE LSD t r Where, MSE is a mean square error, r is the size of equal samples, and v t is the value of t.

Q7. Marks:4

Write down the properties of normal distribution.

The following are the main properties of the normal distribution:

1- Continuous Distribution

The normal probability distribution is a continuous distribution that ranges from to

2- Total Probability

The total area under the normal curve is unity.

3- Mods and Maximum ordinate

The normal probability function is unimodal, its mode is μ and its maximum ordinate at x = μ is

f 

4- Symmetrical Distribution

The normal probability distribution is a symmetrical distribution. Thus i) Mean = Median = Mode ii)

1. 75 0.25

x x Where,  is mean, 0.25 x is 1st Quartile and 0.75 x is 3rd Quartile. iii) All odd order moments about mean are zero.

5- Special areas under the curve

0.6827 i P X

NOTE:

2 ) 0.9545 ii P X

yh total 11 properties hain, marks and time k according

3 ) 0.9973 iii P X

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6- Median, Quartiles, Quartile Deviation

1. 5
2. 25 0.75
3. 75 0.25
4. 25
5. 75 0.75 0.25 0.6745 , 0.6745 0.6745 1.349

x x x x x Q D X

x x x x

7- Variance, Standard Deviation and Mean Deviation

0.7979 Var X S D X

M D X

8- Moments and Moment Ratios

0, 0,

0,

9- Point of Inflexion

The points of inflexion of the normal probability density function are equidistant from mean μ, are at x = μ-σ and x = μ+σ. The normal distribution is a bell shaped distribution.

10- Asymptotic Curve

The normal curve is asymptotic to the xaxis, that is, x grows without bound, the curve get closer and closer to the xaxis but always stay above it.

11- Reproductive Property

If X and X are two independent normal random variables having distributions N  and N 