Question

1. A coin is tossed 3 times. Let x be the random discrete variable representing the number of times tails comes up.

a) Create a sample space for the event;   

b) Create a probability distribution table for the discrete variable x;                

c) Calculate the expected value for x.

2. For the data below, representing a sample of times (in minutes) students spend solving a certain Statistics problem, find P₃₅, range, Q₂ and IQR.

3.0, 3.2, 4.6, 5.2 3.2, 3.5

=> no handwriting. I can't read it correctly.

Answer 1

a.

The sample space for 3 toss is G={ TTT, TTH, THH ,HHH, THT ,HHT ,HTT ,HTH}

|G|=8

Where H=heads T=tails X=no of Tails

Hence sample space for X is S={0,1,2,3}

b.

Probability distribution table

X	no of times X ocuurs in G :(n)	P(X)=n/|G|
0	1	1/8
1	3	3/8
2	3	3/8
3	1	1/8

C.E(X)=0×1/8+1×3/8+2×3/8+3×1/8=12/8=3/2

2.size of sample n=6

The ordered data 3,3.2,3.2,3.5,4.6,5.2

Hence 35% of n is =6×.35=2.1

Now below 3.2 there is only 1 data and and1<2.1 below 3.5 there is 3 data and 3>2.1

Hence 3.2 is p35

Now 1/2 of n is =6/2=3

Now below 3.2 there is only 1 data and 1<3 and below 3.5 there is 3 data and 3=3

Hence 3.2 is the Q2

Also 3/4th of n is=3/4×6=4.5

Below 4.6 there are 4 data and 4<4.5

Below 5.2 there are 5 data and 5>4.5

Hence 4.2 is Q3

1/4 th of n is=6×1/4=1.5

Below 3.2 there are 0 data .and 1<1.5

But below 3.5 there are 3 data .and 3>1.5

Hence Q1 is 3.2

Hence IQR=Q3-Q1=1

Range=maximum-minimum=5.2-3=2.2