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Math  /  Data & Statistics

Questionii) X={0,1,2,3,4,5}X=\{0,1,2,3,4,5\} ialah satu pemboleh ubah rawak diskret dengan kebarangkaliannya ditunjukkan seperti dalam jadual berikut. X={0,1,2,3,4,5}X=\{0,1,2,3,4,5\} is a discrete random variable with its probabilities as shown in the following table. \begin{tabular}{|c|c|c|c|c|c|c|} \hlineX=rX=r & 0 & 1 & 2 & 3 & 4 & 5 \\ \hlineP(X=r)P(X=r) & mm & mm & m−nm-n & 2m2 m & nn & nn \\ \hline \end{tabular}
Jika n=2mn=2 m, cari nilai mm dan nilai nn. If n=2mn=2 m, find the value of mm and of nn. [3 markah / 3 marks]

Studdy Solution

STEP 1

1. The probabilities for a discrete random variable must sum to 1.
2. The relationship between n n and m m is given as n=2m n = 2m .

STEP 2

1. Set up the equation for the sum of probabilities.
2. Substitute the relationship n=2m n = 2m into the equation.
3. Solve for m m .
4. Use the value of m m to find n n .

STEP 3

Write the equation for the sum of probabilities:
m+m+(m−n)+2m+n+n=1 m + m + (m-n) + 2m + n + n = 1

STEP 4

Substitute n=2m n = 2m into the equation:
m+m+(m−2m)+2m+2m+2m=1 m + m + (m - 2m) + 2m + 2m + 2m = 1
Simplify the equation:
m+m+m−2m+2m+2m+2m=1 m + m + m - 2m + 2m + 2m + 2m = 1
6m=1 6m = 1

STEP 5

Solve for m m :
m=16 m = \frac{1}{6}

STEP 6

Use the value of m m to find n n :
n=2m=2×16=13 n = 2m = 2 \times \frac{1}{6} = \frac{1}{3}
The values are:
m=16,n=13 m = \frac{1}{6}, \quad n = \frac{1}{3}

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