Chapter 5, Problem 5.32P

b) The joint probability function for the random variables X and Y is given in Table below. Find a) the marginal probability function of X and Y. P(Y/X) and P(X/Y). c) P(X ≥ 2, Y ≤ 2) y 1 2 3 10.05 0.05 0.1 P(X, Y) = X 20.05 0.1 0.35 3 0 0.2 0.1

Suppose a random variable X as pmf / Px (x) = { %, x = 1, 2, 3, 0, otherwise. find constand c ①P(X = 1), P(X 7,2), PC1 3) C CDF

Suppose that a coin is tossed three so that the sample space is Let X represent the number of heads that can come up. i) Find the probability function corresponding to the random variable X. Assuming that the coin is fair ii) Find the distribution function for the random variable X. iii) Obtain its graph.

Q9 A single-phase transformer, 2500 / 250 V, 50 kVA, 50 Hz has the following parameters, the Primary and secondary resistances are 0.8 ohm and 0.012 ohm respectively, the primary and secondary reactance are 4 ohm and 0.04 ohm respectively and the transformer gives 96% maximum efficiency at 75% full-load. The magnetizing component of-load current is 1.2 A on 2500 V side. 1- Draw the equivalent circuit referred to primary (H.V side) and inserts all the values in it 2- Find out Ammeter, voltmeter and wattmeter readings on open-circuit and short-circuit test. If supply is given to 2500 V side in both cases. Ans. O.C. Test (Vo= 2500 V, lo=1.24 A, Wo=781.25 w) S.C. Test (Vsc =164.924 V, Isc =20 A, Wsc =800 w )

Q2-A)- Enumerate the various losses in transformer. Explain how each loss varies with (Load current, supply voltage). B)- Draw the pharos diagram at load on primary side.

Q2- What are the parameters and loss that can be determined during open-circuit test of singlephase transformer. Draw the circuit diagram of open-circuit test and explain how can you calculate the Parameters and loss.

Q2-Drive the condition of maximum efficiency of single-phase transformer. Q1- A 5 KVA, 500/250 V ,50 Hz, single phase transformer gave the following reading: O.C. Test: 250 V,2 A, 50 W (H.V. side open) S.C. Test: 25 V10 A, 60 W (L.V. side shorted) Determine: i) The efficiency on full load, 0.8 lagging p.f. ii) Draw the equivalent circuit referred to primary and insert all the values it.

Q2- Describe various losses in transformer. Explain how each loss varies with load current, supply voltage

Q1-A 12 KVA, 440/ 220 V, 50 Hz single phase transformer has 275 secondary turns. The no load current of transformer is 2A at power factor 0.375 when connected to 220 V, 50 Hz supply. The full load copper loss is 198.3 watt. Calculate a) Maximum value of flux in the core. b) Maximum efficiency at 0.8 lagging p.f c) KVA supply at maximum efficiency