An automated cyber-security system scans 40 incoming packets for potential malware. For each packet, the probability of correctly identifying a malicious signature, independently of other packets, is 0.2. Let the random variable WWW denote the number of malicious packets correctly identified by the system.
Suggest a suitable distribution for WWW.
In a simplified reward model, the system gains 5 units of 'trust' for each malicious packet correctly identified and loses 2 units of 'trust' for each failure to identify a packet (assuming all 40 packets are actually malicious). Let GGG be the random variable representing the net gain in trust units.
Show that G=7W−80G = 7W - 80G=7W−80.
Find E(G)E(G)E(G) and Var(G)Var(G)Var(G).
Calculate the probability that the system achieves a net gain in trust of at least 5 units.
A high-traffic server processes a larger batch of 200 packets. For this server, the probability of identification is 0.15.
Using a suitable approximation, estimate the probability that the system correctly identifies at least 40 packets in this larger batch.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.