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NDA 1 2024 Maths, question 102

Topic: Probability

Q102

If a random variable (x)(x) follows binomial distribution with mean 55 and variance 44, and 523P(X=3)=λ4λ5^{23}P(X=3)=\lambda4^{\lambda}, then what is the value of λ\lambda ?

  1. (a) 33
  2. (b) 55
  3. (c) 2323Correct answer
  4. (d) 2525

Solution.

Answer: (c) 2323

  1. From np = 5 and np(1 − p) = 4, p = 1/5 and n = 25.
  2. Hence P(X = 3) = C(25, 3)4²²/5²⁵.
  3. Multiplying by 5²³ gives 2300.4²²/25 = 92.4²² = 23.4²³.
  4. Therefore λ = 23, option (c).