What is the probability distribution for the random variable X in this problem?

Click For Summary
SUMMARY

The discussion focuses on determining the probability distribution of a random variable X, representing the attempt at which a professor unlocks a door using one of 17 keys, with only one key being the correct one. The most probable value of X is identified as the attempt where the probability p(x) is maximized. To solve this, participants need to calculate the probabilities P(X = 1), P(X = 2), and so on, based on the selection process of the keys. The discussion emphasizes the necessity of understanding the underlying probability distribution to answer the posed questions effectively.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with random variables and their distributions
  • Knowledge of probability mass functions (PMF)
  • Ability to calculate probabilities for discrete events
NEXT STEPS
  • Study the concept of probability mass functions (PMF) for discrete random variables
  • Learn how to derive the most probable value from a given distribution
  • Explore the binomial distribution and its applications in similar problems
  • Investigate the calculation of standard deviation (σ) in probability distributions
USEFUL FOR

Students studying probability theory, educators teaching statistics, and anyone interested in understanding random variables and their distributions in practical scenarios.

diracdelta
Messages
55
Reaction score
0

Homework Statement


Profesor has 17 keys, and only one unlocks the door.
Let random variable X be attempt at which profesor unlocks the door (key that doesn't work is saved by side)
Find:

a) Most probable value of variable X
b) In which attempt will profesor unlock the door
c) Probability that he will unlock the door between (X- σ) and (X + σ)

The Attempt at a Solution


a)
The most probable value is the x where p(x) is maximum.
How should i find it here? To find maximum i need some type of distribution.
b) This follows after i solve a)
c)also
 
Physics news on Phys.org
diracdelta said:

Homework Statement


Profesor has 17 keys, and only one unlocks the door.
Let random variable X be attempt at which profesor unlocks the door (key that doesn't work is saved by side)
Find:

a) Most probable value of variable X
b) In which attempt will profesor unlock the door
c) Probability that he will unlock the door between (X- σ) and (X + σ)

The Attempt at a Solution


a)
The most probable value is the x where p(x) is maximum.
How should i find it here? To find maximum i need some type of distribution.
b) This follows after i solve a)
c)also

PF rules require you to show some effort at solving the problem.

You need to determine the probabilities ##P(X = 1), P(X = 2), \ldots##, etc. So, to say that the event ##\{X =1\}## occurs, what must happen when the professor selects keys? What is that event's probability? To say that the event ##\{ X = 2\}## occurs, what must happen when the professor selects keys? What would be the probability of that event?

Keep going like that.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
Replies
2
Views
2K