Multiple choice

The probability distribution of a random variable $x$ is a follows: $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $0.05$ $.10$ $.30$ $.20$ $.05$ $.10$ $.05$ $.10$ $.05$ The mean of $x$ is

  1. $1.9$
  2. $5.4$
  3. $3.6$
  4. $6.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mean = sum(x * P(x)). Mean = (2*0.05) + (3*0.10) + (4*0.30) + (5*0.20) + (6*0.05) + (7*0.10) + (8*0.05) + (9*0.10) + (10*0.05) = 0.1 + 0.3 + 1.2 + 1.0 + 0.3 + 0.7 + 0.4 + 0.9 + 0.5 = 5.4.

AI explanation

The mean of a discrete probability distribution is calculated as the sum of each value multiplied by its probability. The sum evaluates to 0.10 + 0.30 + 1.20 + 1.00 + 0.30 + 0.70 + 0.40 + 0.90 + 0.50, which totals 5.40. The mean of the random variable x is 5.4.

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