The distribution of function of random variable

Click For Summary
SUMMARY

The discussion centers on determining the distribution of a random variable derived from a Bernoulli trial, specifically when analyzing a fair coin toss scenario. The user initially plotted the distribution of the variable 'y' but faced confusion regarding the book's solution. The correct probability mass function for a Bernoulli trial is given by PK=Cn(10,k) * p^k * q^(10-k), where p and q represent the probabilities of heads and tails, respectively, both set to 0.5 for a fair coin. The user seeks clarification on their approach versus the book's explanation.

PREREQUISITES
  • Understanding of Bernoulli trials and their probability mass functions
  • Familiarity with probability theory concepts, including random variables
  • Basic skills in plotting distributions and interpreting graphical data
  • Knowledge of combinatorial mathematics, specifically binomial coefficients
NEXT STEPS
  • Study the properties of the binomial distribution in detail
  • Learn about the Central Limit Theorem and its implications for random variables
  • Explore advanced topics in probability theory, such as Markov chains
  • Practice plotting various probability distributions using statistical software
USEFUL FOR

Students in statistics, data analysts, and anyone interested in understanding the behavior of random variables in probability theory.

ecesiu
Messages
7
Reaction score
0
i have this question
image.png

i do find the distribution like this figure :
dis.png

and i plot the y like this:
g_x.png

now i want to find the distribution of y
i tried to take the distribution for each interval in Fx(x) like this :
image.png

but the solution in the book said :
image.png

who is wrong me or the book please help
 
Physics news on Phys.org
Hey ecesiu and welcome to the forums.

You missed out giving us any of the information.
 
which information you mean?
 
Like the solution the book gave, the distribution definition, all the other relevant information: stuff like that.
 
firest i found the density of x which is Bernoulli trial :
PK=Cn(10,k) * p^k * q^(10-k) , k= 0,1,...,10
the distribution is a staircase of the density
which i sketch , the book solution is here :
image.png
 
p=q=0.5 because the coin is fair
where p is the probability of getting head , q is the probability of getting tail
 
So what are you trying to do? Are you trying to figure out whether you think a coin is fair given a number of tosses for heads and tails?
 

Similar threads

Undergrad Linear regression and random variables
  • · Replies 30 ·
2
Replies
30
Views
4K
Undergrad How to show these random variables are independent?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Statistical modeling and relationship between random variables
  • · Replies 7 ·
Replies
7
Views
2K
MHB Distribution and Density functions of maximum of random variables
  • · Replies 6 ·
Replies
6
Views
5K
Undergrad Sampling theory and random sample
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Distribution of Sum of Two Weird Random Variables....
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Failure rate for a uniformly distributed variable
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Randomly Stopped Sums vs the sum of I.I.D. Random Variables
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Random variable vs Random Process
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Random variable and elementary events
  • · Replies 9 ·
Replies
9
Views
2K