Probability distribution

These are the questions that I do not know how to do! Thank you for helping!

In an experiment, a fair cubical dice was rolled repeatedly until a six resulted, and the number of rolls was recorded. The experiment was conducted 60 times.
a)Show that you would expect to get a six on the first roll ten times out of 60 repetitions of the experiment.
b)Find the expected frequency for two rolls correct to one decimal place.

3)The probability districution of the random variable Y is given in the following table, where c is a constant.
y 1, 2, 3, 4, 5
P(Y=y) c, 3c, c^2, c^2, 15/32
Prove that there is only one possible value of c, and state this value.

4)The score S on a spinner is a random variable with distribution given by P(S=s)=k (s=1,2,3,4,5,6,7,8), where k is a constant. Find the value of k.

5)A cubical dice is biased so that the probabilty of any particular score between 1 and 6(inclusive) being obtained is proportional to that score. Find the probability of scoring a 1.

6)For a biased cubical dice the probability of any particular score between 1 and 6 (inclusive) being obtained is inversely proportional to that score. Find the probability of scoring a 1.

Reply 1

steve2005

authecroix123

These are the questions that I do not know how to do! Thank you for helping!

1)The probabilities of the scores on a biased dice are shown in the table below.
Score 1, 2, 3, 4, 5, 6
Probability k, 1/9, 1/9, 1/9, 1/9, 1/2
(a)Find the value of k.

Found k and then saw that you had done it.

Picture 4.png17.2KB

Reply 2

authecroix123

steve2005

Found k and then saw that you had done it.

Are you asking me to show how I get k?
k = 1 - (1/9+1/9+1/9+1/9+1/2)
= 1/18
I want to state again the questions posted here are not all the questions in the book. Those are the questions I do not know how to do. I have done many other questions which I know how to do. Why are all people not believing me and think I didn't do anything and just waiting for the answers?

I now know how to do for the other two parts for question 1 now.

For question 2
I know the part a which is 1/6 x 60 = 10
I am confused at part b because it wants the expected frequency for two rolls, which I do not understand.

For question 3
I do it like this
c + 3c + c^2 + c^2 + 15/32 = 1
4c + 2c^2 = 17/32
Then I am stuck here. I have tried
2c^2 + 4c - 17/32 = 0
62c^2 + 128c -17 = 0
a= 62, b=128 and c=-17
Using the quadractic formula which gives me wrong answer and I am not sure how to solve it and how to prove that there is only one possible value.

4)I don't know what "P(S=s)= k and k is a constant" means. Does it mean that k=1?

5)I don't know what is meant by " the probabilty of any particular score between 1 and 6(inclusive) being obtained is proportional to that score". What is "that score". Any score? And how is the probability proportional to it?

6)Same as question 5 except that it is inversely proportional.

7)Same problem as question 3

Reply 3

Dekota

authecroix123

7)In the following probabilty distribution, c is a constant. Find the value of c.
x 0, 1, 2, 3
P(X=x) 0.6, 0.16, c, c^2

6/10 + 16/100 + c + c² = 1
0.6 + 0.16 + c + c² = 1
c + c² = 24/100
100c² +100c = 24

solve this to get c = -1.2, 0.2

since P(X=x) ≠ -1.2, c = 0.2
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authecroix123

4)The score S on a spinner is a random variable with distribution given by P(S=s)=k (s=1,2,3,4,5,6,7,8), where k is a constant. Find the value of k.