Solve the probability distribution and expectation problem

Click For Summary
The discussion revolves around finding a more efficient method for solving a probability distribution and expectation problem. One participant suggests that calculating the probability of Y=2 by subtracting the probabilities of Y=0 and Y=4 from 1 is a quicker approach. However, concerns are raised about potential errors in this method, as mistakes in calculating Y=0 and Y=4 would directly impact the result for Y=2. An alternative method of finding each probability independently and verifying that their total equals 1 is recommended for accuracy. The conversation emphasizes the balance between efficiency and reliability in probability calculations.
chwala
Gold Member
Messages
2,827
Reaction score
415
Homework Statement
See attached
Relevant Equations
understanding of probability distribution concept...
This is the problem;

1635598062807.png


Find my working to solution below;
1635598109409.png

1635598140494.png
find mark scheme solution below;

1635598182806.png


I seek any other approach ( shorter way of doing it) will be appreciated...
 
Physics news on Phys.org
chwala said:
Homework Statement:: See attached
Relevant Equations:: understanding of probability distribution concept...

shorter way of doing it
It would have been quicker to have found the probability of Y=2 by subtracting the other two probabilities from 1. I don't see any other shortcuts.
 
haruspex said:
It would have been quicker to have found the probability of Y=2 by subtracting the other two probabilities from 1. I don't see any other shortcuts.
That's true, but it could pose problem to a student who may have made a mistake on say finding wrong values of ##Y=0 ##& ##Y=4##, ...if you get what I mean... this error would consequently affect the value of ##Y=2##.
Finding the values of ##Y## indepedently and then checking whether their total sum is ##1## is more concrete...
 
Last edited:

Thread 'Does this series converge uniformly?'

First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...
View full post »

Similar threads

Probability distribution for discrete data
Replies
8
Views
2K
Conditional expectations related to count of event occurring kth time
Replies
2
Views
1K
Solve the variance problem below - statistics
Replies
4
Views
1K
Probability of Hypokalemia w/ 1 or Multiple Measurements
Replies
4
Views
2K
Finding marginal distribution of 2d of probability density function
Replies
6
Views
2K
N-dimensional broken stick problem -- find joint density
Replies
3
Views
985
Finding probability related to Poisson and Exponential Distribution
Replies
6
Views
1K
Finding Probability Density Functions for Independent Random Variables
Replies
2
Views
2K
Find the rejected region in the problem of a biased die - Hypothesis
Replies
2
Views
1K
Solve the probability without replacement problem
Replies
2
Views
1K