Statistics · 3rd secondary · First Term

Random Variables and Probability Distributions — Discrete random variable

About this lesson

This unit introduces discrete random variables and their probability distributions. It begins by defining a random variable as a function from the sample space of a random experiment to the set of real numbers, and explains the concept of a discrete random variable whose range is a finite (countable) set of real numbers. Examples include tossing a coin three times and counting heads, or tossing a die twice and summing the outcomes. The unit then defines the probability distribution function of a discrete random variable, showing how to list probabilities for each possible value, and emphasizes two conditions: each probability is non-negative and the sum of all probabilities equals 1. Worked examples demonstrate constructing probability distribution tables for experiments like tossing coins, drawing cards without replacement, and rolling dice. The unit also covers finding unknown constants in probability distribution formulas and solving related exercises.

Main topics in this lesson

Random variables
Discrete random variables
Probability distribution functions
Finding ranges of random variables
Constructing probability distribution tables
Solving for unknown constants in distributions

Key terms and vocabulary

Random variable
Discrete random variable
Continuous random variable
Probability distribution
Probability distribution function
Sample space
Range
Function
Domain
Co-domain
Mutually exclusive events

Questions and answers on Random Variables and Probability Distributions — Discrete random variable - practice and revision

Multiple choice questions on this lesson in Statistics for 3rd secondary, First Term, with practice exercises for revision and exam preparation.

إذا كان المتغير العشوائي المنفصل X له التوزيع الاحتمالي: P(1)=0.2، P(2)=0.3، P(3)=0.5، فإن P(X ≤ 2) تساوي:

1 0.5
2 0.3
3 0.2
4 0.8

عند إلقاء قطعة نقلة معدنية ثلاث مرات، وكان المتغير العشوائي X هو عدد الصور، فإن P(X=3) تساوي:

1 1/8
2 1/4
3 3/8
4 1/2

إذا كان المتغير العشوائي المنفصل X يأخذ القيم 0، 1، 2، 3، 4 وكان P(X=0)=0.1، P(X=1)=0.2، P(X=2)=0.3، P(X=3)=0.2، فإن P(X=4) تساوي:

1 0.2
2 0.1
3 0.3
4 0.8

إذا كان المتغير العشوائي المنفصل X له التوزيع الاحتمالي: P(0)=0.3، P(1)=0.2، P(2)=0.5، فإن P(X ≥ 1) تساوي:

1 0.7
2 0.5
3 0.2
4 0.3

عند إلقاء حجر نرد مرتين وكان المتغير العشوائي X هو مجموع العددين، فإن أكبر قيمة ممكنة للمتغير X هي:

1 12
2 6
3 11
4 36

إذا كان المتغير العشوائي المنفصل X يأخذ القيم 1، 2، 3، 4 وكان P(X=1)=0.15، P(X=2)=0.25، P(X=3)=0.35، فإن P(X=4) تساوي:

1 0.25
2 0.15
3 0.35
4 0.75

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